Calculus II
This course is a continuation of ACMAT 161, Calculus I.
Outcomes: 1) Select and apply appropriate models and integration techniques to solve problems involving algebraic and transcendental functions; these problems will include but are not limited to applications involving volume, arc length, surface area, force and work; 2) Recognize and implement appropriate techniques to integrate trigonometric functions and apply trigonometric substitutions to solve integrals; 3) Decompose a rational integrand using partial fractions; 4) Evaluate proper and improper integrals using various integration techniques: 5) Determine convergence of improper integrals with discontinuities in their domain or infinite limits of integration; 6) Apply basic anti-differentiation techniques to selected problems arising in various fields such as physical modeling, economics and population dynamics; 7) Find general solutions to basic differential equations and analytical solutions to separable differential equations; 8) Find solutions of various kinds of differential equations using Direction Fields and Euler's Method; 9) Develop the algebra associated with vectors in both two and three dimensions and define two fundamental operations for vectors: the dot product and the cross product; 10) Develop equations for lines and planes in space and explore their properties and uses; 11) Apply familiar single-variable function properties (domain, graphs, limits, continuity and derivatives) to multivariable functions; 12) Find maximum and minimum values of multivariable functions using partial derivatives; 13) Identify the Directional Derivatives and the gradient of a multivariable function.
Outcomes: 1) Select and apply appropriate models and integration techniques to solve problems involving algebraic and transcendental functions; these problems will include but are not limited to applications involving volume, arc length, surface area, force and work; 2) Recognize and implement appropriate techniques to integrate trigonometric functions and apply trigonometric substitutions to solve integrals; 3) Decompose a rational integrand using partial fractions; 4) Evaluate proper and improper integrals using various integration techniques: 5) Determine convergence of improper integrals with discontinuities in their domain or infinite limits of integration; 6) Apply basic anti-differentiation techniques to selected problems arising in various fields such as physical modeling, economics and population dynamics; 7) Find general solutions to basic differential equations and analytical solutions to separable differential equations; 8) Find solutions of various kinds of differential equations using Direction Fields and Euler's Method; 9) Develop the algebra associated with vectors in both two and three dimensions and define two fundamental operations for vectors: the dot product and the cross product; 10) Develop equations for lines and planes in space and explore their properties and uses; 11) Apply familiar single-variable function properties (domain, graphs, limits, continuity and derivatives) to multivariable functions; 12) Find maximum and minimum values of multivariable functions using partial derivatives; 13) Identify the Directional Derivatives and the gradient of a multivariable function.