

Understanding Calculus: Problems, Solutions, and Tips
ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อ
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ซีซัน 1 ตอน 1 - A Preview of Calculus
4 มีนาคม 255333 นาทีCalculus 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 2 - Review - Graphs, Models, and Functions
4 มีนาคม 255330 นาทีIn 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 3 - Review - Functions and Trigonometry
4 มีนาคม 255330 นาทีContinue 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 4 - Finding Limits
4 มีนาคม 255331 นาทีJump 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 5 - An Introduction to Continuity
4 มีนาคม 255331 นาทีBroadly 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 6 - Infinite Limits and Limits at Infinity
4 มีนาคม 255331 นาทีInfinite 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 7 - The Derivative and the Tangent Line Problem
4 มีนาคม 255331 นาทีBuilding 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 8 - Basic Differentiation Rules
4 มีนาคม 255330 นาทีPractice 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 9 - Product and Quotient Rules
4 มีนาคม 255331 นาทีLearn 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 10 - The Chain Rule
4 มีนาคม 255331 นาทีDiscover 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 11 - Implicit Differentiation and Related Rates
4 มีนาคม 255331 นาทีConquer 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).ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 12 - Extrema on an Interval
4 มีนาคม 255330 นาทีHaving 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 13 - Increasing and Decreasing Functions
4 มีนาคม 255331 นาทีUse 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 14 - Concavity and Points of Inflection
4 มีนาคม 255331 นาทีWhat 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 15 - Curve Sketching and Linear Approximations
4 มีนาคม 255332 นาทีBy 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 16 - Applications - Optimization Problems, Part 1
4 มีนาคม 255331 นาทีAttack 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 17 - Applications - Optimization Problems, Part 2
4 มีนาคม 255331 นาทีConclude 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 18 - Antiderivatives and Basic Integration Rules
4 มีนาคม 255331 นาทีUp 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 19 - The Area Problem and the Definite Integral
4 มีนาคม 255331 นาทีOne 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 20 - The Fundamental Theorem of Calculus, Part 1
4 มีนาคม 255330 นาทีThe 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 21 - The Fundamental Theorem of Calculus, Part 2
4 มีนาคม 255331 นาทีTry 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 22 - Integration by Substitution
4 มีนาคม 255332 นาทีInvestigate 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 23 - Numerical Integration
4 มีนาคม 255331 นาทีWhen 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 24 - Natural Logarithmic Function - Differentiation
4 มีนาคม 255331 นาทีReview 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อซีซัน 1 ตอน 25 - Natural Logarithmic Function - Integration
4 มีนาคม 255331 นาทีContinue 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.ทดลองใช้ The Great Courses Signature Collection ฟรีหรือซื้อ