Introduction to Mathematical Physics

1 Infinite series, power series / The Geometric Series / Applications of Series / Convergent and Divergent Series / Testing Series for Convergence; the Preliminary Test / Convergence Tests for Series of Positive Terms: Absolute Convergence / Alternating Series / Conditionally Convergent Series / Power Series; Interval of Convergence / Theorems About Power Series / Expanding Functions in Power Series / Techniques for Obtaining Power Series Expansions / Multiplying a Series by a Polynomial or by Another Series / Division of Two Series or of a Series by a Polynomial / Binomial Series / Substitution of a Polynomial or a Series for the Variable in Another Series / Combination of Methods / Taylor Series Using the Basic Maclaurin Series

2 Vector analysis / Scalars and vectors / Addition and subtraction of vectors / Multiplication by a scalar / Basis vectors and components / Magnitude of a vector / Multiplication of vectors / Equations of lines, planes and spheres / Using vectors to find distances / Reciprocal vectors / Differentiation of vectors / Integration of vectors / Space curves / Vector functions of several arguments / Surfaces / Scalar and vector fields / Vector operators / Vector operator formulae / Cylindrical and spherical polar coordinates / General curvilinear coordinates

3 Complex numbers / Real and Imaginary Parts of a Complex Number / The Complex Plane / Terminology and Notation / Complex Algebra / Complex Infinite Series / Complex Power Series; Disk of Convergence / Elementary Functions of Complex Numbers / Euler’s Formula / Powers and Roots of Complex Numbers / The Exponential and Trigonometric Functions / Hyperbolic Functions / Some Applications

1.1 Mapped to: K1

Define vectors quantities and their properties.

Teaching Strategy Lectures.