MT 182 - Calculus and Analytic Geometry II

• evaluate definite and indefinite integrals by the method of substitution;
• use the integral as the limit of a Riemann sum to solve applied problems involving areas, volumes, arc length, work, surface area and if time permits, liquid pressure and force;
• compute indefinite integrals by “u” substitution, integration by parts, trigonometric and inverse trigonometric substitutions, partial fractions and by use of tables;
• estimate the value of a definite integral by using numeric approximation techniques consisting of: trapezoidal and Simpson’s Rule;
• ascertain whether an integral is improper and determine its convergence or divergence;
• apply appropriate tests to determine the convergence or divergence of sequences and series;
• compute Taylor, Maclaurin, and Power series expansion of certain functions, and where applicable, the derivatives and integrals of these series;
• convert rectangular to polar coordinates and vice versa and sketch graphs in both coordinate systems;
• compute the area under the curve using polar methods;
• convert equations in rectangular and polar form to parametric form and vice versa;
• use a hand held graphing calculator as a tool to reduce computational work and concentrate on the analytic aspects of a variety of problems;
• compute tangent lines and arc lengths using polar coordinates;
• demonstrate the skill to solve growth decay problems and separable differential equations;
• present the derivatives and integrals of the hyperbolic and inverse hyperbolic functions