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May 15, 2024
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MTH 1120 - Calculus II4 lecture hours 0 lab hours 4 credits
Course Description
This course is a continuation of MTH 1110. It focuses on integration methods, parametric and polar equations, and the study of infinite series. Topics include integration by parts, trigonometric integrals, partial fractions, and numerical integration methods, L’Hȏpital’s rule, improper integrals, parametric equations, polar coordinates, vector algebra, sequences, infinite series, power series, Taylor and Maclaurin series, and operations with series. Applications include areas, arc length, volumes, work using integration, and function approximation using Taylor polynomials. (prereq: MTH 1110 ) (quarter system prereq: MA 137)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Evaluate integrals using the method of integration by parts
- Integrate products and powers of trigonometric functions
- Integrate proper and improper rational functions using the method of partial fractions
- Find areas between curves
- Find volumes of solids of revolution using the disk and washer methods
- Use numerical approximation to estimate definite integrals
- Analyze the error of approximation in numerical integration
- Identify indeterminate forms and use L’Hȏpital’s rule to evaluate limits
- Evaluate improper integrals
- Find the arc length of the graph of a function
- Find the work performed by a variable force using integration
- Eliminate the parameter from parametric equations
- Sketch graphs of parametric equations and determine the orientation for increasing parameter
- Find slope and concavity of parameterized curves
- Find arc length of parameterized curves
- Convert between rectangular and polar coordinates
- Sketch graphs of polar curves
- Find slope, area, and arc length in polar coordinates
- Perform vector addition, scalar vector multiplication, and normalization; interpret these operations geometrically
- Find dot and cross products of vectors; interpret these operations geometrically
- Identify the n-th term of a sequence by recognizing a pattern
- Determine if a sequence converges or diverges
- Identify a closed form of the partial sums of a series and evaluate the limit
- Identify a geometric series and evaluate the sum, if convergent
- Apply the divergence test to determine if a series diverges
- Apply the integral test to determine whether a series converges or diverges
- Identify p-series and determine whether the series converges or diverges
- Apply the ratio test to determine whether a series converges or diverges
- Apply convergence tests to determine absolute convergence
- Construct Taylor and Maclaurin series of functions
- Find the interval of convergence of a power series
- Perform algebraic and calculus operations on power series
- Use Taylor and Maclaurin polynomials to approximate functions
Prerequisites by Topic
- Precalculus mathematics
- Limits
- Differentiation of algebraic and transcendental functions
- Definition of the definite integral
- Fundamental theorem of calculus
- Integration by substitution
Course Topics
- Integration by parts
- Trigonometric integrals
- Integration by partial fractions
- Areas between curves
- Volumes using disks and washers
- Numerical integration
- L’Hȏpital’s rule
- Improper integrals
- Arc length
- Work
- Parametric equations
- Polar coordinates and graphs
- Vector addition, scalar vector multiplication, normalization
- Dot and cross products of vectors
- Sequences
- Infinite series and tests for convergence
- Power series and intervals of convergence
- Taylor and Maclaurin series
Coordinator
Dr. Kseniya Fuhrman
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