MATH 162: Calculus II
A continuation of MATH 161. Calculus of logarithmic, exponential, inverse trigonometric, and hyperbolic functions. Techniques of integration. Applications of integration to volume, surface area, arc length, center of mass, and work. Numerical sequences and series. Study of power series and the theory of convergence. Taylor's theorem with remainder.
G.B. Thomas, et al. Thomas' Calculus: Early Transcendentals (Single Variable) (packaged with MyMathLab), 12th ed. Pearson (2009).
ISBN-10: 0-32-170540-8, ISBN-13: 978-0321-70540-2.
Common Syllabus for MATH 162
Review. Prerequisite Material from MATH 161 [1 Week]
Rapid review of differentiation rules.
More detailed review of integration (Ch. 5): areas and distances; the definite integral; the fundamental theorem of calculus.
Chapter 6. Applications of Definite Integrals [2-3 weeks]
Using integrals to calculate volumes of solids, length of curves, surface areas of solids of revolution.
Applications to physics (instructor to select from moments and center of mass, work, fluid pressures and forces).
Chapter 7. Integrals of Transcendental Functions [1 week]
The logarithm defined as an integral.
Exponential functions and hyperbolic functions.
Chapter 8. Techniques of Integration [3 weeks]
Basic integration formulas; integration by parts.
Integration of rational functions by partial fractions; trigonometric integrals; trigonometric substitution.
Integration using tables and computer algebra systems; approximate integration.
Improper integrals of Type I and Type II; comparison tests for convergence of improper integrals.
Chapter 10. Infinite Sequences and Series [4 weeks]
Numerical sequences and series; integral test and estimates of sums; comparison tests.
The ratio and root tests.
Alternating series; absolute and conditional convergence.
Strategy for testing convergence of series; the rearrangement theorem for absolutely convergent series.
Power series; representations of functions as power series.
Taylor and Maclaurin series.
Binomial series; applications of Taylor polynomials; complex numbers and Euler's identity.
Chapter 11. Conic Sections and Polar Coordinates [1-2 weeks]
Rotations, polar coordinates; arc length in polar coordinates.
Conic sections and quadratic equations.
Chapter 9. First Order Differential Equations [as time permits]
Optional: Selected topics from §§ 1 & 2. Solutions, slope fields, Euler's method, first-order linear equations.