Online courses directory (10358)
Sal working through the 53 problems from the practice test available at http://www.cde.ca.gov/ta/tg/hs/documents/mathpractest.pdf for the CAHSEE (California High School Exit Examination). Clearly useful if you're looking to take that exam. Probably still useful if you want to make sure you have a solid understanding of basic high school math. CAHSEE Practice: Problems 1-3. CAHSEE Practice: Problems 4-9. CAHSEE Practice: Problems 10-12. CAHSEE Practice: Problems 13-14. CAHSEE Practice: Problems 15-16. CAHSEE Practice: Problems 17-19. CAHSEE Practice: Problems 20-22. CAHSEE Practice: Problems 23-27. CAHSEE Practice: Problems 28-31. CAHSEE Practice: Problems 32-34. CAHSEE Practice: Problems 35-37. CAHSEE Practice: Problems 38-42. CAHSEE Practice: Problems 43-46. CAHSEE Practice: Problems 47-51. CAHSEE Practice: Problems 52-53. CAHSEE Practice: Problems 1-3. CAHSEE Practice: Problems 4-9. CAHSEE Practice: Problems 10-12. CAHSEE Practice: Problems 13-14. CAHSEE Practice: Problems 15-16. CAHSEE Practice: Problems 17-19. CAHSEE Practice: Problems 20-22. CAHSEE Practice: Problems 23-27. CAHSEE Practice: Problems 28-31. CAHSEE Practice: Problems 32-34. CAHSEE Practice: Problems 35-37. CAHSEE Practice: Problems 38-42. CAHSEE Practice: Problems 43-46. CAHSEE Practice: Problems 47-51. CAHSEE Practice: Problems 52-53.
Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.
Podemos afirmar sin temor a equivocarnos que un buen curso de Cálculo amplía la visión del estudiante en su campo y en su área de estudio, que no pertenece necesariamente al área de física o matemática, por ejemplo en fisiología para estudiantes de medicina.
El Cálculo Diferencial es el lenguaje en el que algunas leyes de la naturaleza se expresan, por ejemplo: nos permite describir el movimiento y el cálculo de trayectorias en dinámica, nos ayuda a resolver problemas de áreas y volúmenes, a resolver problemas extremales en campos como economía y matemática financiera.
En este curso se presentan los conceptos y demostraciones con extrema precisión y cuidado; se hace énfasis en los fundamentos del Cálculo para que lo que se enseña quede fundamentado y claramente explicado.
Se estudia el cálculo diferencial de funciones de variable real, por lo tanto, se parte de una estructura algebraica de los números reales, Se utilizan conceptos puramente métricos, se introduce el concepto de distancia para explicar que nos vamos acercando a algo, es decir, se define la estructura del espacio métrico que da paso al primer tema sucesiones de números reales continúa con sucesiones convergentes, límite funcional, continuidad y la derivada de una función hasta llegar a problemas de aplicación.
Este curso está en modalidad “self-paced”, es decir, “a tu propio ritmo de aprendizaje”. ¿Qué significa esto? Que puedes empezar el curso cuando quieras y seguirlo a tu ritmo ya que no hay fecha prevista de cierre o apertura de lecciones, no sigue un calendario establecido; los trabajos y exámenes no tienen fecha de inicio o entrega, puedes enviarlos en cualquier momento antes de la fecha de finalización del curso.
Esperamos que este curso de Cálculo Diferencial logre cambiar la percepción de los estudiantes en cuanto a su aplicación e importancia.
How does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters? What is the accuracy of a GPS position measurement? How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative.
But what is the derivative? You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative. You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions. You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior. You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.
Learn more about our High School and AP* Exam Preparation Courses
Calculus 1C: Coordinate Systems & Infinite Series
This course was funded in part by the Wertheimer Fund.
*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
How long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.
But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.
1. Modeling the Integral
- Differentials and Antiderivatives
- Differential Equations
- Separation of Variables
2. Theory of Integration
- Mean Value Theorem
- Definition of the Integral and the First Fundamental Theorem
- Second Fundamental Theorem
3. Applications
- Areas and Volumes
- Average Value and Probability
- Arc Length and Surface Area
4. Techniques of Integration
- Numerical Integration
- Trigonometric Powers, Trig Substitutions, Completing the Square
- Partial Fractions, Integration by Parts
This course, in combination with Part 1, covers the AP* Calculus AB curriculum.
This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.
This course was funded in part by the Wertheimer Fund.
Learn more about our High School and AP* Exam Preparation Courses
Calculus 1C: Coordinate Systems & Infinite Series
*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.
How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.
- Changing Perspectives
- Parametric Equations
- Polar Coordinates
- Series and Polynomial Approximations
- Series and Convergence
- Taylor Series and Power Series
This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.
Learn more about our High School and AP* Exam Preparation Courses
This course was funded in part by the Wertheimer Fund.
*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work.
Through a series of case studies, you’ll learn:
- How standardized test makers use functions to analyze the difficulty of test questions;
- How economists model interaction of price and demand using rates of change, in a historical case of subway ridership;
- How an x-ray is different from a CT-scan, and what this has to do with integrals;
- How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks;
- How the Lotka-Volterra predator-prey model was created to answer a biological puzzle;
- How statisticians use functions to model data, like income distributions, and how integrals measure chance;
- How Einstein’s Energy Equation, E=mc2 is an approximation to a more complicated equation.
With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions.
This course provides a unique supplement to a course in single-variable calculus. Key topics include application of derivatives, integrals and differential equations, mathematical models and parameters.
This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms.
This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!
Using Desmos in this Course This course uses Desmos (https://www.desmos.com/), an online graphing calculator, to illustrate examples. Your use of the Desmos platform or any content hosted by Desmos is subject to the Desmos terms of service at https://www.desmos.com/terms and privacy policy at https://www.desmos.com/privacy.
If you do not wish to use the Desmos platform or view content hosted by Desmos, you may not be able to complete the course. This course does NOT require you to make your own individual user account on Desmos. Desmos is a separate entity and is not directly affiliated with HarvardX or edX.
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Videos on a first course in calculus (Differential Calculus).
This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.
Acknowledgement
Prof. McKernan would like to acknowledge the contributions of Lars Hesselholt to the development of this course.
Calculus One is a first introduction to differential and integral calculus, emphasizing engaging examples from everyday life.
Calculus One is a first introduction to differential and integral calculus, emphasizing engaging examples from everyday life.
Calculus Two: Sequences and Series is an introduction to sequences, infinite series, convergence tests, and Taylor series. The course emphasizes not just getting answers, but asking the question "why is this true?"
This is an undergraduate course on differential calculus in one and several dimensions. It is intended as a one and a half term course in calculus for students who have studied calculus in high school. The format allows it to be entirely self contained, so that it is possible to follow it without any background in calculus.
18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.
Sample questions from the A.P. Calculus AB and BC exams (both multiple choice and free answer). 2011 Calculus AB Free Response #1a. 2011 Calculus AB Free Response #1 parts b c d. 2011 Calculus AB Free Response #2 (a & b). 2011 Calculus AB Free Response #2 (c & d). 2011 Calculus AB Free Response #3 (a & b). 2011 Calculus AB Free Response #3 (c). 2011 Calculus AB Free Response #4a. 2011 Calculus AB Free Response #4b. 2011 Calculus AB Free Response #4c. 2011 Calculus AB Free Response #4d. 2011 Calculus AB Free Response #5a. 2011 Calculus AB Free Response #5b. 2011 Calculus AB Free Response #5c.. 2011 Calculus AB Free Response #6a. 2011 Calculus AB Free Response #6b. 2011 Calculus AB Free Response #6c. AP Calculus BC Exams: 2008 1 a. AP Calculus BC Exams: 2008 1 b&c. AP Calculus BC Exams: 2008 1 c&d. AP Calculus BC Exams: 2008 1 d. Calculus BC 2008 2 a. Calculus BC 2008 2 b &c. Calculus BC 2008 2d. 2011 Calculus BC Free Response #1a. 2011 Calculus BC Free Response #1 (b & c). 2011 Calculus BC Free Response #1d. 2011 Calculus BC Free Response #3a. 2011 Calculus BC Free Response #3 (b & c). 2011 Calculus BC Free Response #6a. 2011 Calculus BC Free Response #6b. 2011 Calculus BC Free Response #6c. 2011 Calculus BC Free Response #6d. 2011 Calculus AB Free Response #1a. 2011 Calculus AB Free Response #1 parts b c d. 2011 Calculus AB Free Response #2 (a & b). 2011 Calculus AB Free Response #2 (c & d). 2011 Calculus AB Free Response #3 (a & b). 2011 Calculus AB Free Response #3 (c). 2011 Calculus AB Free Response #4a. 2011 Calculus AB Free Response #4b. 2011 Calculus AB Free Response #4c. 2011 Calculus AB Free Response #4d. 2011 Calculus AB Free Response #5a. 2011 Calculus AB Free Response #5b. 2011 Calculus AB Free Response #5c.. 2011 Calculus AB Free Response #6a. 2011 Calculus AB Free Response #6b. 2011 Calculus AB Free Response #6c. AP Calculus BC Exams: 2008 1 a. AP Calculus BC Exams: 2008 1 b&c. AP Calculus BC Exams: 2008 1 c&d. AP Calculus BC Exams: 2008 1 d. Calculus BC 2008 2 a. Calculus BC 2008 2 b &c. Calculus BC 2008 2d. 2011 Calculus BC Free Response #1a. 2011 Calculus BC Free Response #1 (b & c). 2011 Calculus BC Free Response #1d. 2011 Calculus BC Free Response #3a. 2011 Calculus BC Free Response #3 (b & c). 2011 Calculus BC Free Response #6a. 2011 Calculus BC Free Response #6b. 2011 Calculus BC Free Response #6c. 2011 Calculus BC Free Response #6d.
Minima, maxima, and critical points. Rates of change. Optimization. Rates of change. L'Hopital's rule. Mean value theorem. Minima, maxima and critical points. Testing critical points for local extrema. Identifying minima and maxima for x^3 - 12x - 5. Concavity, concave upwards and concave downwards intervals. Recognizing concavity exercise. Recognizing concavity. Inflection points. Graphing using derivatives. Another example graphing with derivatives. Minimizing sum of squares. Optimizing box volume graphically. Optimizing box volume analytically. Optimizing profit at a shoe factory. Minimizing the cost of a storage container. Expression for combined area of triangle and square. Minimizing combined area. Rates of change between radius and area of circle. Rate of change of balloon height. Related rates of water pouring into cone. Falling ladder related rates. Rate of change of distance between approaching cars. Speed of shadow of diving bird. Mean Value Theorem. Introduction to L'H
Divergence theorem intuition. Divergence theorem examples and proofs. Types of regions in 3D. 3-D Divergence Theorem Intuition. Divergence Theorem Example 1. Why we got zero flux in Divergence Theorem Example 1. Type I Regions in Three Dimensions. Type II Regions in Three Dimensions. Type III Regions in Three Dimensions. Divergence Theorem Proof (part 1). Divergence Theorem Proof (part 2). Divergence Theorem Proof (part 3). Divergence Theorem Proof (part 4). Divergence Theorem Proof (part 5). 3-D Divergence Theorem Intuition. Divergence Theorem Example 1. Why we got zero flux in Divergence Theorem Example 1. Type I Regions in Three Dimensions. Type II Regions in Three Dimensions. Type III Regions in Three Dimensions. Divergence Theorem Proof (part 1). Divergence Theorem Proof (part 2). Divergence Theorem Proof (part 3). Divergence Theorem Proof (part 4). Divergence Theorem Proof (part 5).
Volume under a surface with double integrals. Triple integrals as well. Double Integral 1. Double Integrals 2. Double Integrals 3. Double Integrals 4. Double Integrals 5. Double Integrals 6. Triple Integrals 1. Triple Integrals 2. Triple Integrals 3. Double Integral 1. Double Integrals 2. Double Integrals 3. Double Integrals 4. Double Integrals 5. Double Integrals 6. Triple Integrals 1. Triple Integrals 2. Triple Integrals 3.
Indefinite integral as anti-derivative. Definite integral as area under a curve. Integration by parts. U-substitution. Trig substitution. Antiderivatives and indefinite integrals. Indefinite integrals of x raised to a power. Antiderivative of hairier expression. Basic trig and exponential antiderivatives. Antiderivative of x^-1. Simple Riemann approximation using rectangles. Generalizing a left Riemann sum with equally spaced rectangles. Rectangular and trapezoidal Riemann approximations. Trapezoidal approximation of area under curve. Riemann sums and integrals. Deriving integration by parts formula. Antiderivative of xcosx using integration by parts. Integral of ln x. Integration by parts twice for antiderivative of (x^2)(e^x). Integration by parts of (e^x)(cos x). U-substitution. U-substitution example 2. U-substitution Example 3. U-substitution with ln(x). Doing u-substitution twice (second time with w). U-substitution and back substitution. U-substitution with definite integral. (2^ln x)/x Antiderivative Example. Another u-substitution example. Riemann sums and integrals. Intuition for Second Fundamental Theorem of Calculus. Evaluating simple definite integral. Definite integrals and negative area. Area between curves. Area between curves with multiple boundaries. Challenging definite integration. Introduction to definite integrals. Definite integrals (part II). Definite Integrals (area under a curve) (part III). Definite Integrals (part 4). Definite Integrals (part 5). Definite integral with substitution. Introduction to trig substitution. Another substitution with x=sin (theta). Integrals: Trig Substitution 1. Trig and U substitution together (part 1). Trig and U substitution together (part 2). Trig substitution with tangent. Integrals: Trig Substitution 2. Integrals: Trig Substitution 3 (long problem). Fundamental theorem of calculus. Applying the fundamental theorem of calculus. Swapping the bounds for definite integral. Both bounds being a function of x. Proof of Fundamental Theorem of Calculus. Connecting the first and second fundamental theorems of calculus. Introduction to improper integrals. Improper integral with two infinite bounds. Divergent improper integral. Antiderivatives and indefinite integrals. Indefinite integrals of x raised to a power. Antiderivative of hairier expression. Basic trig and exponential antiderivatives. Antiderivative of x^-1. Simple Riemann approximation using rectangles. Generalizing a left Riemann sum with equally spaced rectangles. Rectangular and trapezoidal Riemann approximations. Trapezoidal approximation of area under curve. Riemann sums and integrals. Deriving integration by parts formula. Antiderivative of xcosx using integration by parts. Integral of ln x. Integration by parts twice for antiderivative of (x^2)(e^x). Integration by parts of (e^x)(cos x). U-substitution. U-substitution example 2. U-substitution Example 3. U-substitution with ln(x). Doing u-substitution twice (second time with w). U-substitution and back substitution. U-substitution with definite integral. (2^ln x)/x Antiderivative Example. Another u-substitution example. Riemann sums and integrals. Intuition for Second Fundamental Theorem of Calculus. Evaluating simple definite integral. Definite integrals and negative area. Area between curves. Area between curves with multiple boundaries. Challenging definite integration. Introduction to definite integrals. Definite integrals (part II). Definite Integrals (area under a curve) (part III). Definite Integrals (part 4). Definite Integrals (part 5). Definite integral with substitution. Introduction to trig substitution. Another substitution with x=sin (theta). Integrals: Trig Substitution 1. Trig and U substitution together (part 1). Trig and U substitution together (part 2). Trig substitution with tangent. Integrals: Trig Substitution 2. Integrals: Trig Substitution 3 (long problem). Fundamental theorem of calculus. Applying the fundamental theorem of calculus. Swapping the bounds for definite integral. Both bounds being a function of x. Proof of Fundamental Theorem of Calculus. Connecting the first and second fundamental theorems of calculus. Introduction to improper integrals. Improper integral with two infinite bounds. Divergent improper integral.
Limit introduction, squeeze theorem, and epsilon-delta definition of limits. Introduction to limits. Limit at a point of discontinuity. Determining which limit statements are true. Limit properties. Limit example 1. Limits 1. One-sided limits from graphs. One-sided limits from graphs. Introduction to Limits. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits. Limits 1. Limits and infinity. Limits at positive and negative infinity. More limits at infinity. Limits with two horizontal asymptotes. Limits 2. Squeeze Theorem. Proof: lim (sin x)/x. Limit intuition review. Building the idea of epsilon-delta definition. Epsilon-delta definition of limits. Proving a limit using epsilon-delta definition. Limits to define continuity. Continuity. Epsilon Delta Limit Definition 1. Epsilon Delta Limit Definition 2. Introduction to limits. Limit at a point of discontinuity. Determining which limit statements are true. Limit properties. Limit example 1. Limits 1. One-sided limits from graphs. One-sided limits from graphs. Introduction to Limits. Limit Examples (part 1). Limit Examples (part 2). Limit Examples (part 3). Limit Examples w/ brain malfunction on first prob (part 4). More Limits. Limits 1. Limits and infinity. Limits at positive and negative infinity. More limits at infinity. Limits with two horizontal asymptotes. Limits 2. Squeeze Theorem. Proof: lim (sin x)/x. Limit intuition review. Building the idea of epsilon-delta definition. Epsilon-delta definition of limits. Proving a limit using epsilon-delta definition. Limits to define continuity. Continuity. Epsilon Delta Limit Definition 1. Epsilon Delta Limit Definition 2.
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