Mathematics For SE II

Course #SE1002

Est.imated Completion Time: 3 months

Overview

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

Prerequisites

  • SE1001

Learning Outcomes

At the end of this course, the student shall demonstrate the ability to:
  • 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 ODEIdentify 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.
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Application Deadlines

  •  08 Jul 2024

    Fall Quarter applications due

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