

Understanding Calculus: Problems, Solutions, and Tips
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Episódios
T1 EP.1 – A Preview of Calculus
4 de março de 201033 minCalculus is the mathematics of change, a field with many important applications in science, engineering, medicine, business, and other disciplines. Begin by surveying the goals of the series. Then get your feet wet by investigating the classic tangent line problem, which illustrates the concept of limits.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.2 – Review - Graphs, Models, and Functions
4 de março de 201030 minIn the first of two review episodes on precalculus, examine graphs of equations and properties such as symmetry and intercepts. Also explore the use of equations to model real life and begin your study of functions, which Professor Edwards calls the most important concept in mathematics.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.3 – Review - Functions and Trigonometry
4 de março de 201030 minContinue your review of precalculus by looking at different types of functions and how they can be identified by their distinctive shapes when graphed. Then review trigonometric functions, using both the right triangle definition as well as the unit circle definition, which measures angles in radians rather than degrees.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.4 – Finding Limits
4 de março de 201031 minJump into real calculus by going deeper into the concept of limits introduced in the first episode. Learn the informal, working definition of limits and how to determine a limit in three different ways: numerically, graphically, and analytically. Also discover how to recognize when a given function does not have a limit.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.5 – An Introduction to Continuity
4 de março de 201031 minBroadly speaking, a function is continuous if there is no interruption in the curve when its graph is drawn. Explore the three conditions that must be met for continuity, along with applications of associated ideas, such as the greatest integer function and the intermediate value theorem.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.6 – Infinite Limits and Limits at Infinity
4 de março de 201031 minInfinite limits describe the behavior of functions that increase or decrease without bound, in which the asymptote is the specific value that the function approaches without ever reaching it. Learn how to analyze these functions, and try some examples from relativity theory and biology.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.7 – The Derivative and the Tangent Line Problem
4 de março de 201031 minBuilding on what you've learned about limits and continuity, investigate derivatives, which are the foundation of differential calculus. Develop the formula for defining a derivative, and survey the history of the concept and its different forms of notation.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.8 – Basic Differentiation Rules
4 de março de 201030 minPractice several techniques that make finding derivatives relatively easy: the power rule, the constant multiple rule, sum and difference rules, plus a shortcut to use when sine and cosine functions are involved. Then see how derivatives are the key to determining the rate of change in problems involving objects in motion.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.9 – Product and Quotient Rules
4 de março de 201031 minLearn the formulas for finding derivatives of products and quotients of functions. Then use the quotient rule to derive formulas for the trigonometric functions not covered in the previous episode. Also investigate higher-order derivatives, differential equations, and horizontal tangents.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.10 – The Chain Rule
4 de março de 201031 minDiscover one of the most useful of the differentiation rules, the chain rule, which allows you to find the derivative of a composite of two functions. Explore different examples of this technique, including a problem from physics that involves the motion of a pendulum.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.11 – Implicit Differentiation and Related Rates
4 de março de 201031 minConquer the final strategy for finding derivatives: implicit differentiation, used when it's difficult to solve a function for y. Apply this rule to problems in related rates (for example, the rate at which a camera must move to track the space shuttle at a specified time after launch).Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.12 – Extrema on an Interval
4 de março de 201030 minHaving covered the rules for finding derivatives, embark on the first of five episodes dealing with applications of these techniques. Derivatives can be used to find the absolute maximum and minimum values of functions, known as extrema, a vital tool for analyzing many real-life situations.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.13 – Increasing and Decreasing Functions
4 de março de 201031 minUse the first derivative to determine where graphs are increasing or decreasing. Next, investigate Rolle's theorem and the mean value theorem, one of whose consequences is that during a car trip, your actual speed must correspond to your average speed during at least one point of your journey.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.14 – Concavity and Points of Inflection
4 de março de 201031 minWhat does the second derivative reveal about a graph? It describes how the curve bends, whether it is concave upward or downward. Determine concavity much as you found the intervals where a graph was increasing or decreasing, except this time you'll use the second derivative.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.15 – Curve Sketching and Linear Approximations
4 de março de 201032 minBy using calculus, you can be certain that you have discovered all the properties of the graph of a function. After learning how this is done, focus on the tangent line to a graph, which is a convenient approximation for values of the function that lie close to the point of tangency.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.16 – Applications - Optimization Problems, Part 1
4 de março de 201031 minAttack real-life problems in optimization, which requires finding the relative extrema of different functions by differentiation. Calculate the optimum size for a box, and the largest area that can be enclosed by a circle and a square made from a given length of wire.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.17 – Applications - Optimization Problems, Part 2
4 de março de 201031 minConclude your investigation of differential calculus with additional problems in optimization. For success with such word problems, Professor Edwards stresses the importance of first framing the problem with precalculus, reducing the equation to one independent variable, and then using calculus to find and verify the answer.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.18 – Antiderivatives and Basic Integration Rules
4 de março de 201031 minUp until now, you've calculated a derivative based on a given function. Discover how to reverse the procedure and determine the function based on the derivative. This approach is known as obtaining the antiderivative, or integration. Also learn the notation for integration.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.19 – The Area Problem and the Definite Integral
4 de março de 201031 minOne of the classic problems of integral calculus is finding areas bounded by curves. This was solved for simple curves by the ancient Greeks. See how a more powerful method was later developed that produces a number called the definite integral, and learn the relevant notation.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.20 – The Fundamental Theorem of Calculus, Part 1
4 de março de 201030 minThe two essential ideas of this course, derivatives and integrals, are connected by the fundamental theorem of calculus, one of the most important theorems in mathematics. Get an intuitive grasp of this deep relationship by working several problems and surveying a proof.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.21 – The Fundamental Theorem of Calculus, Part 2
4 de março de 201031 minTry examples using the second fundamental theorem of calculus, which allows you to let the upper limit of integration be a variable. In the process, explore more relationships between differentiation and integration, and discover how they are almost inverses of each other.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.22 – Integration by Substitution
4 de março de 201032 minInvestigate a straightforward technique for finding antiderivatives, called integration by substitution. Based on the chain rule, it enables you to convert a difficult problem into one that's easier to solve by using the variable u to represent a more complicated expression.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.23 – Numerical Integration
4 de março de 201031 minWhen calculating a definite integral, the first step of finding the antiderivative can be difficult or even impossible. Learn the trapezoid rule, one of several techniques that yield a close approximation to the definite integral. Then do a problem involving a plot of land bounded by a river.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.24 – Natural Logarithmic Function - Differentiation
4 de março de 201031 minReview the properties of logarithms in base 10. Then see how the so-called natural base for logarithms, e, has important uses in calculus and is one of the most significant numbers in mathematics. Learn how such natural logarithms help to simplify derivative calculations.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compreT1 EP.25 – Natural Logarithmic Function - Integration
4 de março de 201031 minContinue your investigation of logarithms by looking at some of the consequences of the integral formula developed in the previous episode. Next, change gears and review inverse functions at the precalculus level, preparing the way for a deeper exploration of the subject in coming episodes.Assine os canais The Great Courses Signature Collection ou The Great Courses Signature Collection & Living, ou compre