ENGR1180 - Engineering Mathematics I

Credits: 03

Dr. Shanaz Wahid	email:Shanaz.Wahid@sta.uwi.edu
Mr. Oral Robertson	email:Oral.Robertson@sta.uwi.edu

Vector Calculus (Corral)

Linear Algebra (Dawkins)

Calculus II (Dawkins)

Just the Maths (Hobson)

Differential Equations (Dawkins)

 

Note: the three Dawkins texts may also be obtained from Paul's Online Math Notes.

Week	Topics	References
1	Plane and space vectors, vector equations of lines and planes, dot product, cross product	Sections 1.1-1.5 of Vector Calculus (Corral)
2	Geometric interpretation of linear equations, Gaussian elimination,  n-dimensional space, definition of a vector space	Pages 3-26, 126-135, 154-155, 183-184 of Linear Algebra (Dawkins)
3	Span and subspace, linear dependence, basis, dimension, basic properties of matrices	Pages 193-228, 27-38  of  Linear Algebra (Dawkins)
4	Transpose, determinants, rank and its application to linear systems, matrix inversion by cofactors	Pages 43-52, 107-114  of  Linear Algebra (Dawkins)
5	Convergence of series, comparison and ratio tests, Maclaurin and Taylor series	Pages 179-201, 211-218, 230-234, 254, 269-278  of  Calculus II (Dawkins)
6	Definition and properties of a complex number, complex roots of a quadratic equation, complex numbers as vectors, modulus and argument, product and quotients	Units 6.1, 6.2, 6.3 of Just the Maths (Hobson)
7	De Moivre’s theorem, exponential form, hyperbolic functions, loci in the Argand diagram	Units 6.4, 6.5, 6.6 of Just the Maths (Hobson)
8	Definitions, direction fields, linear first order differential equations, separable differential equations	Pages 2-18, 21-44 of  Differential Equations (Dawkins)
9	Modelling with first order equations, exact equations, numerical approximations, homogeneous second order equations with constant coefficients	Pages 77-84, 45-55, 94-101, 104-112 of  Differential Equations (Dawkins)
10	Fundamental solutions, complex and repeated roots of the characteristic equation, reduction of order, method of undetermined coefficients	Pages 113-130, 137-155 of  Differential Equations (Dawkins)
11	Variation of parameters, mechanical and electrical vibrations, higher order homogeneous differential equations	Pages 156-173, 350-354 of  Differential Equations (Dawkins)

Assignment 1	Vectors
Assignment 2	Gaussian Elimination and Vector Spaces
Assignment 3	Matrices
Assignment 4	Series and Taylor Series (updated Sep 2 2011)
Assignment 5	Complex Numbers I
Assignment 6	Complex Numbers II
Assignment 7	Differential Equations I (updated Sep 2 2011)
Assignment 8	Differential Equations II (updated Sep 5 2011)
Assignment 9	Differential Equations III

Sample final examination

Solutions

July 2012	Solutions
Dec 2011	Solutions

Vectors

Basic revision of vectors -- component form, length of a vector, vector addition and scalar multiplication, dot product, angle between two vectors, orthogonal vectors, scalar and vector projections, cross product, scalar triple product	Tisdell Vectors I
Visually understanding basic vector operations	Khan Vectors I
Parametric equations of lines	Khan Vectors II
Defining a plane in R^3 with a point and normal vector	Khan Vectors III
Figuring out a normal vector to a plane from its equation	Khan Vectors IV
Distance between a point and a plane in three dimensions	Khan Vectors V

 

Linear Algebra

Geometric interpretation of a linear system in two dimensions	Khan Linear Algebra I
Geometric interpretation of a linear system in three dimensions	Khan Linear Algebra II
Solving a system of linear equations by using an augmented matrix (infinite number of solutions)	Khan Linear Algebra III
Another example of using an augmented matrix (unique solution)	Khan Linear Algebra IV
A third example of using an augmented matrix (no solution)	Khan Linear Algebra V
Linear combinations and spans of vectors	Khan Linear Algebra VI
Introduction to linear independence	Khan Linear Algebra VII
More on linear independence	Khan Linear Algebra VIII
Determining whether 3 vectors are linearly independent and/or span R^3	Khan Linear Algebra IX
Introduction to linear subspaces of R^n	Khan Linear Algebra X
Understanding the definition of a basis of a subspace	Khan Linear Algebra XI

 

Matrices

What a matrix is. How to add and subtract them.	Khan Matrices I
Multiplying two 2x2 matrices	Khan Matrices II
More on multiplying matrices	Khan Matrices III
Identity matrix; introduction to matrix inverses; formula for inverse of a 2 x 2 matrix; determinant of a 2 x 2 matrix	Khan Matrices IV
Determinants of 2 x2 and 3 x 3 matrices	Khan Matrices V
Inverting a 3x3 matrix	Khan Matrices VI
Using the inverse of a matrix to solve a system of equations	Khan Matrices VII
Transpose of a matrix	Khan Matrices VIII
Taking the transpose of the product of two matrices	Khan Matrices IX
Transposes of sums and inverses	Khan Matrices X

 

Series

Sigma notation, introduction to series, n^th partial sum, convergence, geometric series, telescoping series, n^th term test, integral test (not required)	Tisdell Series I
Comparison, limit comparison and ratio tests for series	Tisdell Series II
Taylor polynomials (a.k.a. polynomial approximations); material after the 24^th minute is not required	Tisdell Series I
Taylor and Maclaurin series	Tisdell Series I

 

Complex numbers

i and Imaginary Numbers	Khan Complex Numbers I
Adding, subtracting and multiplying complex numbers	Khan Complex Numbers II
Dividing complex numbers; argument of a complex number	Tisdell Complex Numbers I
Calculations using the polar form of complex numbers	Tisdell Complex Numbers II
Sketching regions in the complex plane	Tisdell Complex Numbers III
n^th roots of a complex number	Tisdell Complex Numbers IV
Application of complex numbers to trigonometric identities	Tisdell Complex Numbers V

 

Differential equations

Introduction to ordinary differential equations	Tisdell Differential Equations I
First order linear differential equations	Tisdell Differential Equations II
Separable differential equations	Tisdell Differential Equations III
Modelling with differential equations (an example of a mixing problem)	Tisdell Differential Equations IV
Geometric interpretation of y'=f(x,y), direction fields, integral curves, plotting direction fields via isoclines, integral curves don't cross, integral curve cannot touch because of uniqueness, consequence of noncontinuity in uniqueness and existence	Mattuck Differential Equations I
Euler method (modified Euler methods such as Runge-Kutta are not required)	Mattuck Differential Equations II
Introduction to first order homogenous equations	Khan Differential Equations I
Exact differential equations	Tisdell Differential Equations V
Second order differential equations (homogeneous)	Tisdell Differential Equations VI
Solution to a 2nd order, linear homogeneous ODE with repeated roots	Tisdell Differential Equations VII
Second order differential equations (inhomogeneous) using the method of undetermined coefficents	Tisdell Differential Equations VIII
An example of the reduction of order method	Khan Differential Equations II
Mechanical vibration example; variation of parameters example	Tisdell Differential Equations IX
Second-order linear homogeneous ode's: superposition, uniqueness, Wronskians	Mattuck Differential Equations III

Element	Required to pass course	Weighting	Number of Assessment Artefacts
Final Exam	No	60%	1
Assignments	No	5%	9
Midterms	No	35%	2
TOTAL	Yes	100%	12