Boyce and DiPrima, which is the book for this course, can be found online here. This is the 9th edition, but it is almost identical to the 10th edition.
Mid-term examination 1: Worked answers here.
Mid-term examination 2: Worked answers here.
General (non-homework) Links
Homework 12: Set Wednesday 26th November. ONLY 1 HOMEWORK QUESTION (due Monday 1st December, between 09:00 and 14:00 outside LSK203, or hand in on Friday 28th November in class). The rest of the questions are more challenging practice questions, with answers here.
Broad-brush lecture outline, week by week
Relevant section numbers in Boyce and DiPrima given in square brackets 
Week 1 (to Friday 5th September): Main concept: Introduction to differential equations.Terminology of differential equations [1.3]
Week 2 (to Friday 12th September): Main concept: First-order ODEs, and how to solve them. How to solve separable equations [2.2] and using the method of integrating factors [2.1]. Being able to convert from words to math [2.3]. Difference between linear/non-linear equations [2.4]. Autonomous equations: how to learn about the nature of the solutions without having to solve the equation [2.5].
Week 3 (to Friday 19th September): Main concept: (Linear) Second-order ODEs, and how to solve them. Method for solving homogeneous linear second-order equations with constant coefficients [3.1]. Some general theory for homogeneous linear second-order equations - the Wronskian, and the concept of 'fundamental sets of solutions' [3.2]. Solving equations with either complex roots [3.3], or repeated roots [3.4].
Week 4 (to Friday 26th September): Main concept: (Linear) Second-order ODEs: Solutions for non-homogeneous equations. Finish material on repeated roots of equations, and general theory for finding a second root by 'reduction of order' [3.4]. Non-homogeneous equations: Method of undetermined coefficients [3.5]; and Method of variation of parameters [3.6]. Mathematical modelling: applications of 2nd-order DEs [3.7-3.8] (briefly).
Week 5 (to Friday 3rd October): Main concept: Finish off 2nd-order ODEs, (maybe) start thinking about Systems of Equations, (definitely) sit 1st mid-term exam. Finish Method of variation of parameters [3.6], and briefly mention Mathematical Modelling [3.7-3.8]. Summarize before exam. (maybe) Start looking at systems of linear equations [7.1]
Week 6 (to Friday 10th October): Main concept: Systems of linear 1st-order equations: basic ideas, homogeneous problems with distinct real roots. Review of basic linear algebra: eigenvectors and eigenvalues [7.2-7.4], homogeneous systems of 1st-order equations: distinct real roots and the concept of phase portraits [7.5], complex roots [7.6].
Week 7 (to Friday 17th October): Main concept: Systems of linear 1st-order equations: homogeneous systems with repeated roots. Finish complex roots [7.6], (briefly) definition of fundamental matrix [7.7], start repeated roots [7.8]. Note: there is no class on either Monday 13th or Wednesday 15th.
Week 8 (to Friday 24th October): Main concept: Systems of linear 1st-order equations: repeated roots, and non-homogeneous systems. Repeated roots [7.8], non-homogeneous equations [7.9] - three methods for solving these: undetermined coefficients; diagonalisation; or variation of parameters.
Week 9 (to Friday 31st October): Main concept: Laplace transforms. Basic definition and some simple Laplace transforms [6.1]; application to ODEs [6.2]; use with step functions and application to ODEs with discontinuous forcing [6.3,6.4].
Week 10 (to Friday 7th November): Main concept: More Laplace transforms, and introduction to PDEs. Impulse functions (Dirac delta function) [6.5] and convolution [6.6]. Begin partial differential equations [chapter 7] - basic ideas [7.1].
Week 11 (to Friday 14th November): Main concept: Fourier Series. Boundary value problems, eigenfunctions/eigenvalues [7.1]; Fourier series: periodicity, odd/even functions, orthogonality, method for calculating Fourier series [7.2 - 7.4].
Week 12 (to Friday 21st November): Main concept: MID-TERM 2. Separation of variables for PDEs. Finish Fourier series [10.3,10.4]. Separation of variables: diffusion equation (heat conduction) [10.5,10.6].
Week 13 (to Friday 28th November): Main concept: Separation of variables for PDEs Wave equation (vibrations of a string) [10.7], Laplace's equation [10.8]. END OF COURSE.
Contact me: drh39 'at' cam.ac.uk