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Recognize equations of lines and planes in 3D-space and be able to represent them algebraically.
Calculate dot and cross products and apply the techniques to solve problems that arise in physics. Represent and operate vectors geometrically and algebraically. Convert between polar and Cartesian coordinates and graph polar equations. Perform basic geometry in the 3D-rectangular coordinate system. Determine the radius and interval of convergence for a given power series. Compute Taylor and Maclaurin series for differentiable functions and provide effective polynomial approximations of differentiable functions. Apply appropriate tests and theorems to determine convergence/divergence of series including the divergence test, the integral test, comparison tests, p-series test, the alternating series test, and ratio test. Determine whether sequences converge or diverge and find the limits of convergent sequences. Distinguish between a sequence and a series. Apply integral calculus to solve application problems such as areas, volumes, arc length, average value of a function, work done by a variable force, center of mass of a lamina, and rectilinear motions. Determine the convergence or divergence of improper integrals, and evaluate convergent improper integrals. Approximate values of definite integrals using numerical methods, including Simpson’s and trapezoid rules. Use various integration techniques proficiently, including the substitution rule, integration by parts, trigonometric substitution, partial fractions, and the techniques for integrating powers of trigonometric functions, roots of binomials, and inverse trigonometric functions. Upon successful completion of this course, students should be able to:
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