This course provides an introduction to selected pre- and post-calculus topics. Covered will be complex numbers, matrix algebra, and differential equations.

• Complex Numbers
• Understand the notion of a complex number.
• Apply the algebra of complex numbers (add, subtract, multiply, and divide).
• Understand the geometry of complex numbers.
• Understand and use the complex conjugate.
• Understand and compute the magnitude of a complex number.
• Use the trigonometric form of complex numbers.
• Apply De Moivre's Theorem.
• Apply Euler's Formula.
• Sequences and Series
• Understand the notion of a sequence.
• Understand the limiting behavior of sequences.
• Given a sequence, determine whether or not it converges, and if it does, find the limit.
• Understand the concept and notation of a series
• Be able to recognize a geometric, p-, and harmonic series.
• Determine the convergence of a series by appropriate tests, including the integral, comparison, alternating series , ratio, and root 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.
• Matrix Algebra
• Write a system of linear equations in matrix form and describe the nature of the solutions.
• Perform algebraic operations on matrices: addition, subtraction, multiplication, and multiplication by a constant.
• Compute the determinant of a square matrix using cofactor expansion.
• Describe the basic properties of determinants.
• Use Cramer's rule to solve small systems (not larger than 3x3) of linear equations.
• Ordinary Linear Differential Equations {Up to Second Order)
• Classify a given DE as ordinary or partial; determine its order; and whether it's linear or not.
• Verify whether a given function is a solution of a DE.
• Recognize and solve a first order linear ODE. Identify the homogeneous and non-homogenous term in the solution obtained.
• Recognize and solve a separable first order ODE.
• Formulate and solve appropriate applied problems involving elementary mechanics.
• Find solutions to a second order ODE with constant coefficients.
• Solve appropriate applied problems for mechanical or electrical oscillations.