Understanding Calculus II Problems Solutions and Tips [RU UL RG]

Understanding Calculus II - Problems, Solutions, and Tips

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Genre: Mathematics, Calculus | Language: English

Calculus II is the payoff for mastering Calculus I. This second course in the calculus sequence introduces you to exciting new techniques and applications of one of the most powerful mathematical tools ever invented. Equipped with the skills of Calculus II, you can solve a wide array of problems in the physical, biological, and social sciences, engineering, economics, and other areas. Success at Calculus II also gives you a solid foundation for the further study of mathematics, and it meets the math requirement for many undergraduate majors.

Lectures

01 Basic Functions of Calculus and Limits
02 Differentiation Warm-up
03 Integration Warm-up
04 Differential Equations桮rowth and Decay
05 Applications of Differential Equations
06 Linear Differential Equations
07 Areas and Volumes
08 Arc Length, Surface Area, and Work
09 Moments, Centers of Mass, and Centroids
10 Integration by Parts
11 Trigonometric Integrals
12 Integration by Trigonometric Substitution
13 Integration by Partial Fractions
14 Indeterminate Forms and L'H?pital's Rule
15 Improper Integrals
16 Sequences and Limits
17 Infinite Series桮eometric Series
18 Series, Divergence, and the Cantor Set
19 Integral Test桯armonic Series, p-Series
20 The Comparison Tests
21 Alternating Series
22 The Ratio and Root Tests
23 Taylor Polynomials and Approximations
24 Power Series and Intervals of Convergence
25 Representation of Functions by Power Series
26 Taylor and Maclaurin Series
27 Parabolas, Ellipses, and Hyperbolas
28 Parametric Equations and the Cycloid
29 Polar Coordinates and the Cardioid
30 Area and Arc Length in Polar Coordinates
31 Vectors in the Plane
32 The Dot Product of Two Vectors
33 Vector-Valued Functions
34 Velocity and Acceleration
35 Acceleration's Tangent and Normal Vectors
36 Curvature and the Maximum Bend of a Curve