Single Variable Calculus II with Matrix Algebra

Course #MA1114

Est.imated Completion Time: 5 weeks

Overview

Topics in calculus include applications of integration, special techniques of integration, infinite series, convergence tests, and Taylor series. Matrix algebra topics covered are: the fundamental algebra of matrices including addition, multiplication of matrices, multiplication of a matrix by a constant and a column (vector) by a matrix; elementary matrices and inverses, together with the properties of these operations; solutions to mxn systems of linear algebraic equations using Gaussian elimination and the LU decomposition (without pivoting); determinants, properties of determinants; and a brief introduction to the arithmetic of complex numbers and DeMoivre's theorem. Taught at the rate of nine hours per week for five weeks.

Prerequisites

MA1113

Learning Outcomes

Use integration to find the area between curves; find volumes of solids of revolution; find total work done in appropriate problems; find the average value of a function.
Evaluate appropriate integrals by using trigonometric identities and trigonometric substitution.
Use the method of partial fractions to evaluate integrals of rational functions.
Recognize improper integrals, determine whether they converge, and if possible, evaluate them.
Determine whether or not a sequence converges and if it does, find its limit.
Determine whether or not a series converges by appropriate tests, including the ratio, comparison, p-series, and alternating series tests.
Find the interval of convergence for a power series.
Apply Taylor’s Theorem to find polynomial approximations to given functions and estimate their accuracy.
Perform arithmetic operations on complex numbers (addition, subtraction, multiplication, division, raising to powers), determine the magnitude, argument, real part, imaginary part, complex conjugate, and convert between rectangular and polar coordinates.
Apply De Moivre’s Theorem; find nth roots of complex numbers; state Euler’s formula.
Use Gauss-Jordan elimination to find the general solution for a linear system with m equations and n unknown variables, determine the type of solution set (inconsistent, unique solution, or infinitely many solutions) by Gauss elimination.
Perform algebraic operations on matrices and vectors: addition, subtraction, scalar multiplication, matrix multiplication and transposition.
Define and describe the basic properties of the inverse of a matrix and find the inverse of a square matrix using Gauss-Jordan method.
Compute the determinant of a square matrix either by elementary row operations (EROs) or by cofactor expansion.
Use Cramer’s rule (where applicable) to solve small systems of linear equations. Explain why Cramer’s rule is inappropriate for large systems.
Find the eigenvalues and associated eigenvectors of square matrices, including cases of repeated or complex eigenvalues.

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