Elementary Calculus | Department of Mathematics

Elementary Calculus

Core course for B.Sc. (Research) Biotechnology. Only available as UWE with prior permission of Department of Mathematics. Does not count towards a Minor in Mathematics.

Credits (Lec:Tut:Lab): (3:1:0)

Overview: This course is targeted at undergraduates who did not take Mathematics at +2 level in school, and now need to quickly acquire basic calculus skills in order to satisfy their major requirements. For example, the purpose may be to enable them to take a Probability course which requires basic concepts from calculus. The course will emphasize geometric meaning rather than formal proof.

Students who need greater rigour, as well as more computational skills, should take MAT101 Calculus I.

Detailed Syllabus:

  1. Functions: Real line and its subsets, real functions, graphs, polynomials, rational functions, real powers, trigonometric functions, roots, boundedness, monotonicity, composition of functions, inverse functions.
  2. Limits and Continuity: Algebra of limits, left and right limits, limits involving infinity, continuity, left and right continuity, types of discontinuity.
  3. Differentiation: Rates of change, tangents to graphs, first and higher derivatives, algebra of differentiation, chain rule, exponentials and logarithms.
  4. Applications of differentiation: Exponential growth and decay, intervals of increase and decrease, first and second derivative tests, curve sketching.
  5. Integration: Definite and indefinite integrals, Fundamental Theorem of Calculus, substitution, integration by parts, trigonometric integrals, improper integrals.
  6. First-Order Differential Equations: Separable differential equations, logistic growth.

References:

  1. Short Calculus, by Serge Lang, Springer.
  2. Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.

Past Instructors: L M Saha

Course Code: 
MAT020
Course Credits: 
4.00
Department: 
Course Level: