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MATH1120:
Mathematics for Engineering, Science and Technology 2
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Contents
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I
Calculus
1
CA1: Maclaurin Series
Introduction
Infinite Series
Maclaurin Series
2
CA2: Taylor Series
Generating New Series from Known Series
Taylor Series
3
CA3: Functions of Several Variables
Functions of Two Variables
Level Curves
Surfaces of Revolution
Functions of 3 (or more) Variables
4
CA4: Partial Differentiation
Partial Differentiation
Higher Partial Derivatives
5
CA5: Linear Approximations
Tangent Planes
Linear Approximations
Quadratic Approximations
6
CA6: The Directional Derivative
Directional Derivatives
In Three Variables
7
CA7: Local and Global Extrema
Critical Points
Second Derivative Test
Global Extrema
8
CA8: Chain Rules
The Single Variable Chain Rule
Multivariable Chain Rules
Implicit Differentiation
II
Differential Equations
9
DE1: Introduction
Introduction
Direction Fields and Euler's Method
10
DE2: First Order Separable DEs
First Order Separable DEs
Some Simple Applications of First Order Separable DEs
Partial Fraction Decomposition
11
DE3: First Order Linear DEs
Exact First Order DEs
First Order Linear DEs
Some Simple Applications of First Order Linear DEs
12
DE4: Homogeneous Second Order Linear DEs
Homogeneous Second Order Linear DEs With Constant Coefficients
13
DE5: Non-Homogeneous Second Order Linear DEs
Non-Homogeneous First Order Linear DEs
The Method of Undetermined Coefficients
14
DE6: An Application of Second Order Linear DEs with Constant Coefficients
A Simple Model
Adding Damping
Adding an External Force
III
Linear Algebra
15
LA1: Systems of Linear Equations
Introduction
Matrices and Systems of Linear Equations
Solving Systems of Linear Equations
16
LA2: Geometric Interpretations of Linear Equations
Interpretation Via Rows
Interpretation Via Columns
17
LA3: Matrix Algebra
Addition and Scalar Multiplication
Matrix Multiplication
Matrices and Systems of Linear Equations
Linear Transformations
18
LA4: Square Matrices
Inverse Matrices
Determinants
19
LA5: Eigenvalues and Eigenvectors
Introduction
Finding Eigenvalues and Eigenvectors
A Simple Application
20
LA6: Some Applications of Eigenvalues and Eigenvectors
Powers of Matrices
Coupled Linear Differential Equations
Authored in PreTeXt
Chapter
16
LA2: Geometric Interpretations of Linear Equations
16.1
Interpretation Via Rows
16.2
Interpretation Via Columns