Syllabus for Mathematics for Information Science 1

Module 1: Differential calculus

Contact hours: 9

1. Limits and continuity

   • Limits of function values
   • Continuity at a point and continuity of functions

2. Rates of change and derivatives

   • Derivative at a point and as a function
   • Second and higher-order derivatives
   • Instantaneous rates of change
   • Chain rule and implicit differentiation

3. Applications of derivatives

   • Tangents and normal lines
   • Linearization
   • Concavity and the second-derivative test for concavity

Module 2: Functions of several variables

Contact hours: 9

1. Functions of two or more variables

   • Domains and ranges
   • Level curves
   • Limits and continuity

2. Partial derivatives

   • Partial derivatives of functions of two or more variables
   • Partial derivatives and continuity
   • Second-order partial derivatives
   • Mixed derivative theorem

3. Multivariable chain rule

   • Chain rule for functions of two variables

Module 3: Directional derivatives and extrema

Contact hours: 9

1. Directional derivatives and gradient

   • Chain rule for functions of three variables
   • Directional derivatives in the plane
   • Interpretation and properties of the directional derivative
   • Gradient

2. Local extreme values

   • Relative extrema and critical points
   • Saddle points
   • First- and second-derivative tests for local extrema

3. Absolute extrema

   • Absolute maxima and minima on closed, bounded regions

Module 4: Optimization and linear programming

Contact hours: 9

1. Constrained optimization

   • Constrained maxima and minima
   • Lagrange multipliers with one constraint
   • Lagrange multipliers with two constraints

2. Further methods

   • Steepest descent for two variables

3. Linear programming

   • Formulation of a linear programming problem
   • Graphical solution method

Course objectives

1. Use calculus to study functions of several variables, identify extrema, and solve optimization problems.

Course outcomes

1. Linearize functions and analyze concavity.
2. Find limits and partial derivatives of multivariable functions.
3. Interpret directional derivatives and solve multivariable maxima and minima.
4. Solve constrained optimization and graphical linear programming problems.

Assessment

Continuous Internal Evaluation (CIE)

• Attendance — 5 marks

• Assignment or microproject — 15 marks

• Two written internal examinations — 10 marks each

End-Semester Examination (ESE): 60 marks

• Part A: Eight questions, two from each module, carrying 3 marks each (24 marks). Answer all.

• Part B: Two questions from each module; answer one full question from each module. Each carries 9 marks (36 marks).

• Examination duration: 2 hours 30 minutes.