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 afunction.

· Evaluate appropriate integrals by using trigonometric identities and trigonometricsubstitution.

· Use the method of partial fractions to evaluate integrals of rational functions.

· Recognize improper integrals, determine whether they converge, and if possible, evaluatethem.

· Determine whether or not a sequence converges and if it does, find its limit.

· Determine whether or not a series converges by appropriate tests, includingtheratio,comparision,p-seris,andalternatingseriestests.

· Findtheintervalofconvergenceforapowerseries.

· 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 polarcoordinates.

· Apply De Moivre’s Thorem; find nth roots of complex numbers; state Euler’sformula.

· 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 Gausselimination.

· Perform algebraic operations on matrices and vectors: addition, subtraction, scalar multiplication, matrix multiplication andtransposition.

· Define and describe the basic properties of the inverse of a matrix, and findtheinverseofasquarematrixusingGauss-Jordanmethod.

· Compute the determinant of a square matrix either by elementary row operations (EROs) or by cofactorexpansion.

· 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 complexeigenvalues.

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