Understanding Calculus II: Problems, Solutions, and Tips
Where to Watch Understanding Calculus II: Problems, Solutions, and Tips
36.
Curvature and the Maximum Bend of a Curve
2013-05-31
See how the concept of curvature helps with analysis of the acceleration vector. Come full circle by using ideas from elementary calculus to determine the point of maximum curvature.
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35.
Acceleration's Tangent and Normal Vectors
2013-05-31
Use the unit tangent vector and normal vector to analyze acceleration. The unit tangent vector points in the direction of motion.
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34.
Velocity and Acceleration
2013-05-31
Combine parametric equations, curves, vectors, and vector-valued functions to form a model for motion in the plane. In the process, derive equations for the motion of a projectile subject to gravity.
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33.
Vector-Valued Functions
2013-05-31
Use your knowledge of vectors to explore vector-valued functions, which are functions whose values are vectors. The derivative of such a function is a vector tangent to the graph that points in the direction of motion.
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32.
The Dot Product of Two Vectors
2013-05-31
Deepen your skill with vectors by exploring the dot product method for determining the angle between two nonzero vectors. Then turn to projections of one vector onto another.
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31.
Vectors in the Plane
2013-05-31
Begin a series of episodes on vectors in the plane by defining vectors and their properties, and reviewing vector notation. Then learn how to express an arbitrary vector in terms of the standard unit vectors.
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30.
Area and Arc Length in Polar Coordinates
2013-05-31
Continue your study of polar coordinates by focusing on applications involving integration. First, develop the polar equation for the area bounded by a polar curve.
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29.
Polar Coordinates and the Cardioid
2013-05-31
In the first of two episodes on polar coordinates, review the main properties and graphs of this specialized coordinate system. Consider the cardioids, which have a heart shape.
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28.
Parametric Equations and the Cycloid
2013-05-31
Parametric equations consider variables such as x and y in terms of one or more additional variables, known as parameters. This adds more levels of information, especially orientation, to the graph of a parametric curve.
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27.
Parabolas, Ellipses, and Hyperbolas
2013-05-31
Review parabolas, ellipses, and hyperbolas, focusing on how calculus deepens our understanding of these shapes. First, look at parabolas and arc length computation.
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26.
Taylor and Maclaurin Series
2013-05-31
Finish your study of infinite series by exploring in greater depth the Taylor and Maclaurin series. Discover that you can calculate series representations in many ways.
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25.
Representation of Functions by Power Series
2013-05-31
Learn the steps for expressing a function as a power series. Experiment with differentiation and integration of known series.
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24.
Power Series and Intervals of Convergence
2013-05-31
Discover that a power series can be thought of as an infinite polynomial. The key question with a power series is to find its interval of convergence.
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23.
Taylor Polynomials and Approximations
2013-05-31
Try out techniques for approximating a function with a polynomial. The first example shows how to construct the first-degree Maclaurin polynomial for the exponential function.
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22.
The Ratio and Root Tests
2013-05-31
Finish your exploration of convergence tests with the ratio and root tests. The ratio test is particularly useful for series having factorials, whereas the root test is useful for series involving roots to a given power.
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21.
Alternating Series
2013-05-31
Having developed tests for positive-term series, turn to series having terms that alternate between positive and negative. See how to apply the alternating series test.
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20.
The Comparison Tests
2013-05-31
Develop more convergence tests, learning how the direct comparison test for positive-term series compares a given series with a known series. The limit comparison test is similar but more powerful, since it allows analysis of a series without having a term-by-term comparison with a known series.
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19.
Integral Test - Harmonic Series, p-Series
2013-05-31
Does the celebrated harmonic series diverge or converge? Discover a proof using the integral test. Then generalize to define an entire class of series called p-series, and prove a theorem showing when they converge. Close with the sum of the harmonic series, the fascinating Euler-Mascheroni constant, which is not known to be rational or irrational.
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18.
Series, Divergence, and the Cantor Set
2013-05-31
Explore an important test for divergence of an infinite series: If the terms of a series do not tend to zero, then the series diverges. Solve a bouncing ball problem.
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17.
Infinite Series - Geometric Series
2013-05-31
Look at an example of a telescoping series. Then study geometric series, in which each term in the summation is a fixed multiple of the previous term.
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16.
Sequences and Limits
2013-05-31
Start the first of 11 episodes on one of the most important topics in Calculus II: infinite series. The concept of an infinite series is based on sequences, which can be thought of as an infinite list of real numbers.
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15.
Improper Integrals
2013-05-31
So far, you have been evaluating definite integrals using the fundamental theorem of calculus. Study integrals that appear to be outside this procedure.
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14.
Indeterminate Forms and L'Hôpital's Rule
2013-05-31
Revisit the concept of limits from elementary calculus, focusing on expressions that are indeterminate because the limit of the function may not exist. Learn how to use L'Hopital's famous rule for evaluating indeterminate forms, applying this valuable theorem to a variety of examples.
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13.
Integration by Partial Fractions
2013-05-31
Put your precalculus skills to use by splitting up complicated algebraic expressions to make them easier to integrate. Learn how to deal with linear factors, repeated linear factors, and irreducible quadratic factors.
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12.
Integration by Trigonometric Substitution
2013-05-31
Trigonometric substitution is a technique for converting integrands to trigonometric integrals. Evaluate several cases, discovering that you can conveniently represent these substitutions by right triangles.
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11.
Trigonometric Integrals
2013-05-31
Explore integrals of trigonometric functions, finding that they are often easy to evaluate if either sine or cosine occurs to an odd power. If both are raised to an even power, you must resort to half-angle trigonometric formulas.
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10.
Integration by Parts
2013-05-31
Begin a series of episodes on techniques of integration, also known as finding antiderivatives. After reviewing some basic formulas from Calculus I, learn to develop the method called integration by parts, which is based on the product rule for derivatives.
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9.
Moments, Centers of Mass, and Centroids
2013-05-31
Study moments and centers of mass, developing formulas for finding the balancing point of a planar area, or lamina. Progress from one-dimensional examples to arbitrary planar regions.
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8.
Arc Length, Surface Area, and Work
2013-05-31
Continue your exploration of the power of integral calculus. First, review arc length computations. Then, calculate the areas of surfaces of revolution. Close by surveying the concept of work, answering questions such as, how much work does it take to lift an object from Earth's surface to 800 miles in space?
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7.
Areas and Volumes
2013-05-31
Use integration to find areas and volumes. Begin by trying your hand at planar regions bounded by two curves.
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6.
Linear Differential Equations
1970-01-01
Investigate linear differential equations, which typically cannot be solved by separation of variables. The key to their solution is what Professor Edwards calls the "magic integrating factor.
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5.
Applications of Differential Equations
2013-05-31
Continue your study of differential equations by examining orthogonal trajectories, curves that intersect a given family of curves at right angles. These occur in thermodynamics and other fields.
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4.
Differential Equations - Growth and Decay
2013-05-31
In the first of three episodes on differential equations, learn various techniques for solving these very useful equations, including separation of variables and Euler's method, which is the simplest numerical technique for finding approximate solutions. Then look at growth and decay models, with two intriguing applications.
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3.
Integration Warm-up
2013-05-31
Complete your review by going over the basic facts of integration. After a simple example of integration by substitution, turn to definite integrals and the area problem.
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2.
Differentiation Warm-up
2013-05-31
In your second warm-up episode, review the concept of derivatives, recalling the derivatives of trigonometric, logarithmic, and exponential functions. Apply your knowledge of derivatives to the analysis of graphs.
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1.
Basic Functions of Calculus and Limits
2013-05-31
Learn what distinguishes Calculus II from Calculus I. Then embark on a three-episode review, beginning with the top 10 student pitfalls from precalculus.
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Understanding Calculus II: Problems, Solutions, and Tips is a series categorized as a new series. Spanning 1 seasons with a total of 36 episodes, the show debuted on 2013. The series has earned a no reviews from both critics and viewers. The IMDb score stands at undefined.
How to Watch Understanding Calculus II: Problems, Solutions, and Tips
How can I watch Understanding Calculus II: Problems, Solutions, and Tips online? Understanding Calculus II: Problems, Solutions, and Tips is available on The Great Courses Signature Collection with seasons and full episodes. You can also watch Understanding Calculus II: Problems, Solutions, and Tips on demand at Amazon Prime, Amazon online.
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The Great Courses Signature Collection
Cast
Bruce H. Edwards
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