# SE1002: Mathematics For SE II - NPS Online

## 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 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.

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