ENGR1180  Engineering Mathematics I

Credits: 03 
Dr. Shanaz Wahid  email:Shanaz.Wahid@sta.uwi.edu 
Mr. Oral Robertson  email:Oral.Robertson@sta.uwi.edu 
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 1.11.5 of Vector Calculus (Corral) 
2 
Geometric interpretation of linear equations, Gaussian elimination, ndimensional space, definition of a vector space  Pages 326, 126135, 154155, 183184 of Linear Algebra (Dawkins) 
3 
Span and subspace, linear dependence, basis, dimension, basic properties of matrices  Pages 193228, 2738 of Linear Algebra (Dawkins) 
4 
Transpose, determinants, rank and its application to linear systems, matrix inversion by cofactors  Pages 4352, 107114 of Linear Algebra (Dawkins) 
5 
Convergence of series, comparison and ratio tests, Maclaurin and Taylor series  Pages 179201, 211218, 230234, 254, 269278 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 218, 2144 of Differential Equations (Dawkins) 
9 
Modelling with first order equations, exact equations, numerical approximations, homogeneous second order equations with constant coefficients  Pages 7784, 4555, 94101, 104112 of Differential Equations (Dawkins) 
10 
Fundamental solutions, complex and repeated roots of the characteristic equation, reduction of order, method of undetermined coefficients  Pages 113130, 137155 of Differential Equations (Dawkins) 
11 
Variation of parameters, mechanical and electrical vibrations, higher order homogeneous differential equations  Pages 156173, 350354 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 
Dec 2012  Solutions 
July 2012  Solutions 
Dec 2011  Solutions 
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 RungeKutta 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 
Secondorder 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 