MTH 264 Calculus II (4 cr.)
Prepares students for further study in calculus with analytic geometry by providing them with the necessary competencies in finding limits, differentiation, and integration. Continues the study of calculus of algebraic and transcendental functions, including rectangular, polar, and parametric graphing, indefinite and definite integrals, methods of integration,
and power series along with applications. Designed for mathematical, physical, and engineering science programs. This course replaces MTH 174 or MTH 176 or MTH 274 and is the second course in a three-course sequence. Prerequisite: Placement in MTH 264 or completion of MTH 263 or equivalent with a grade of C or better. Lecture 4 hours per week.
Major Topics:
Application of Integration
Techniques of Integration
Infinite Sequences and Series
Parametric curves and Polar Coordinates
Objectives and Skills:
Compute Volumes by cross-section method
Compute Volumes by disk-washer method
Compute Volumes by shell method
Compute Work (spring, rope)
Compute Work (pumping liquids)
Compute Arc length
Compute Areas of surfaces of revolution
Compute Center of mass
Integrate by parts
Calculate trigonometric integrals
Calculate integrals by trigonometric substitution
Define the indeterminate forms and apply L’Hopital’s Rule
Calculate improper integrals
Integrate by partial fractions
Integrate using Tables and Software
Approximate integrals (Trapezoidal, Simpson) with error estimation
Define of and understand Sequences
Define of and understand Series
Determine convergence by integral test
Determine convergence by comparison test
Determine convergence of alternating series
Determine absolute convergence (ratio, root tests)
Apply strategies for testing series
Work with power series
Represent functions as power series
Calculate Taylor and Maclaurin series
Represent curves by parametric equations
Perform calculus with parametric curves
Graph functions in polar system
Calculate areas and lengths in polar coordinates
Define conic forms in polar form