MA1E022: Engineering Mathematics II (for JF)
Notes
Some (not all) parts of the course notes will be in the form of a handout or will be available here. All will be in PDF format and require a programme such as Adobe Acrobat Reader to read them.
Refer also to the textbooks.
- 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. Basic ideas about higher dimensions.
- 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.
- 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).
- 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).
- Chapter 5. Infinite series
- (Chapter 9 in Anton's Calculus.) Sequences and their limits. Series, some tests for convergence. Power series.
- Chapter 6. Linear equations
- (In Chapter 1 of Anton, Linear algebra) Gaussian elimnation and Gauss-Jordan elimination.
- 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.
- Chapter 8. Determinants
- (In Chapter 2 of Anton, Linear algebra) Determinants by cofactor expansions. Calculation by row reduction. Cramer's rule.