MA1E02: Engineering Mathematics II
Books for Hilary Term 2018
Calculus: Late Transcendetals 10th edition, Howard Anton, Irl C. Bivens, Stephen Davis
Elementary Linear Algebra – with Supplementary applications 11th ediition , Howard Anton and Chris Rorres
(ISBN: 9781119046264) is a bundle made for this module containing both books plus online codes for both.
Here is a Link for the part of this module relating to Calculus Late Transcendentals on Wiley Plus.com and here a link for Elementary Linear Algebra (which WileyPlus considers a different "course").
The information above has been updated for 2018, but the details below will not all be applicable in 2018. They will be updated later.
- Chapter 1. Vectors
- (Chapter 11 in Anton's Calculus.) This deals with vectors from a geometrical point of view (arrows) first. Then a more algebraic approach (with components). Equations of lines and planes in space. Cross products. [So we covered pretty much what is in sections 11.1 to 11.6 with some differences or omissions.] Basic ideas about higher dimensions. [This is maybe more like section 3.2 of the Linear Algebra book, but we pretty much skimmed this.]
- Chapter 2. Exponential and Log functions
- (Chapter 6 in Anton's Calculus.) This deals with the exponential function $\exp(x) = e^x$ and its inverse the natural logarithm function $\ln x$. Also other functions, the inverse trigonometric functions and the hyperbolic functions. [We omitted section 6.4 and took a differnet approach in places, but more or less covered the rest of Chapter 6.]
- Chapter 3. Techniques of integration
- (Chapter 7 in Anton's Calculus.) We recall first what integration is and the technique of substitution. Then integration by parts, trigonometric integrals (powers of $\sin x$ times powers of $\cos x$), inverse trig substitutions, partial fractions. Then improper integrals and how computers can evaluate integrals (computer algebra systems and basic ideas for numerical evaluation of definite integrals). [We covered most of the Chapter but there are more details in the book than what we covered.]
- Chapter 4. Differential equations
- (Chapter 8 in Anton's Calculus.) Besides some general explanations about what differential equations are and where they arise, we just consider two kinds that can be solved easily: variables separable and first order linear (constant coefficient). [This is mostly sections 8.2 and 8.4, but again without all details.]
- Chapter 5. Infinite series
- (Chapter 9 in Anton's Calculus.) Sequences and their limits. Series, some tests for convergence. Power series. [We covered a good bit of section 9.1 to 9.5 and the rest of the chapter in a rather cursory fashion.]
- Chapter 6. Linear equations
- (In Chapter 1 of Anton, Linear algebra) Gaussian elimnation and Gauss-Jordan elimination. [More or less sections 1.1 and 1.2.]
- Chapter 7. Matrices
- (In Chapter 1 of Anton, Linear algebra) Matrices, matrix multiplication, inverse matrices, elementary matrices and their connection to elementary row operations, finding inverses, special matrices (diagonal, triangular, symmetric, nilpotent), trace of a square matrix. [More or less sections 1.3 to 1.7.]
- Chapter 8. Determinants
- (In Chapter 2 of Anton, Linear algebra) Determinants by cofactor expansions. Calculation by row reduction. Cramer's rule. [More or less the 3 sections of Chapter 2.]