MATH1082 — Single Variable Calculus II
MATH 1082 - Single Variable Calculus II MATH 1082 - Single Variable Calculus II Hours/Week: Lecture 5 Lab 0 Course Description: This is the second course in the two-semester sequence of Single Variable Calculus. Topics include techniques of integration, applications of the definite integral, numerical integration, improper integrals, infinite sequences and series, Taylor series representations, parametric curves, polar curves, and elementary differential equations. A graphing calculator is required. Instruction will be provided in the use of the TI-84 calculator. This course is intended for students majoring in chemistry, engineering, physics, science, mathematics, mathematics education, and computer science. MnTC Goals 4 Mathematics/Logical Reasoning Major Content 1. The Definite Integral a. Fundamental Theorem of Calculus b. Mean Value Theorem for Integrals c. Average value of a function 2. Numerical Integration a. Left and right sums b. Trapezoidal rule c. Midpoint sums d. Simpson’s rule e. Error calculations 3. Applications of the Definite Integral a. Area between curves b. Volume i. Cross-sections ii. Discs and washers iii. Shells c. Work d. Arc length e. Surface area f. Fluid force g. Probability h. Center of Mass 4. Techniques of Integration a. Substitution b. Integration by parts c. Trigonometric integration d. Partial fraction decomposition e. Trigonometric substitution 5. Improper integrals a. Convergence or divergence b. Indeterminate forms c. L’Hospital’s rule 6.
Prerequisites: MATH1081
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