MT171: One Variable Calculus and Differential Equations
for non-majors – 2021/2022
Course Outline
1. Review of Techniques of Integration (6 hours)
The indefinite and definite integrals
Integration theorems (without proofs), integration by parts
Integration of powers of trigonometric functions
Integration by substitution, by partial fractions.
Evaluation of improper integrals
Applications.
2. Differential Equations (12 hours)
Meaning of solution, first order differential equations
Graphical solution, separation of variables
Homogeneous and reducible to homogeneous differential equations
Exact and reducible to exact differential equations
Linear initial value problems
Second order differential equations with constant coefficients
Second order differential equations with variable coefficients (e.g. Bessel, Leg-
endre Differential Equations).
3. Sequences (3 hours)
Sequences, convergence, sum, product and quotients
4. Numerical Methods (9 hours)
Zeros of a function; secant, Regula Falsi, Newton-Raphson methods
Iteration finite differences; numerical differentiation and integration
Numerical methods for ordinary differential equations; the Euler method, the
modified Euler method, the Runge-Kutta method (without derivation)
The trapezoidal rule with derivation, the Simpson rule (without derivation);
Computer applications
5. Infinite Series (6 hours)
Infinite series; convergence, tests for convergence
Power series; convergence, differentiation and integration of power series
Taylor series, Maclaurin series
Approximation of function, Cherbyshev polynomials
Applications.
1
6. Fourier Series (9 hours)
Periodic function, odd and even functions
Fourier series, Half range Fourier sine and cosine series
Analytic and numerical methods for finding Fourier coefficients
Application to science and engineering.
Delivery: 45 hours of lectures and 15 hours of tutorials (online or offline, depends on
your group).
Offline groups: tutorial is a session where by a tutor meets with the students to
discuss difficult tasks or special techniques in solving the tasks, and therefore a student
is supposed to solve all the tasks before the tutorial session. A student can also be asked
to present his/her solution.
Online groups: Students with have weekly tutorials as well as 10 Quizzes, where
solutions will be submitted through learning management system lms.udsm.ac.tz.
The teaching schedule is:
Day/Time 08:00–09:00 14:00–15:00 17:00–18:00
Monday Yombo 4
Tuesday Yombo 4
Thursday Yombo 4
Assessments: 40% course-work; two tests, 10 Quizzes and 60% Final Examination.
TEXT BOOKS
1. S. T. Tan. Single Variable Calculus. Early Transcendentals. Brooks/Cole, Cengage
Learning, Canada 2011.
2. Boyce E. B, & DiPrima R. C. Elementary Differential Equations and Boundary
Value Problems, John Wiley & Sons, Inc., New York, 2001.
3. E. Kreyzig; Advanced Engineering Mathematics (10th ed.). John Wiley & Sons,
INC. 2011.
4. R. L. Burden and J. D. Faires. Numerical Analysis, 9th ed. Brooks/Cole, 2011.
5. Ross S. L. Introduction to Ordinary Differential Equations, John Willy & Sons, New
York, 1989.
6. A. C. Bajipai, I. M. Calus & J. A. Fairley: Mathematics for Engineers and Scientists
Vol. I, II.
7. M. K. Jain, S. R. Iyengar & R. K. Jain: Numerical Methods for Scientific and
Engineering Computation
