This course has three parts - integration, sequences and series, and ordinary differential equations. We will first introduce two basic techniques of integration - substitution rule and integration by parts, and then through various examples, we will systematically develope these into formidable tools. Next, we will move on to studying infinite sequences, and their summations. The aim is to introduce Taylor series, which serves as an extension of the idea of derivatives as first order (linear) approximation to the function. Differential equations, that is equations involving an unknown function and its derivatives, are ubiquitous in applications of mathematics to "real world" problems. Any mathematical model of a process involving rates of change can usually be formulated in terms of a differential equation. In the last part of this course, we will study some natural differential equations that arise in examples ranging from population models, mixing problems to springs and electric circuits, and use the techniques developed in the first two parts of the course to solve such equations.
Assignment-1 (due 09/08/15)
Assignment-2 (due 09/15/15)
Assignment-3 (due 09/29/15)
Assignment-4 (due 10/06/15)
Assignment-5 (due 10/13/15)
Assignment-6 (due 10/20/15)
Assignment-7 (due 10/27/15)
Assignment-8 (due 11/10/15)
Assignment-9 (due 11/17/15)
Assignment-10 (due 11/24/15)
Assignment-11 (due 12/08/15)
Practice problems for first mid-term
Here is the first midterm and the solutions
Practice problems for the second mid-term
Here is the second midterm and the solutions
Practice problems for the final exam