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BSc. CSIT First Semester Mathematics I (Calculus) Course Overview

 

First Semester Mathematics I (Calculus) Course Overview

Title Mathematics I (Calculus)
Course code MTH112
Nature of course Theory
Semester First-Semester
Full marks 80 + 20
Pass marks 32 + 8
Credit Hrs 3
Elective/Compulsory Compulsory


Study Materials:

Notes Books Old Questions

Course Description:

The course covers the concepts of functions, limits, continuity, differentiation, integration of function of one variable; logarithmic, exponential, applications of derivative and antiderivatives, differential equations, vectors and applications, partial derivatives and Multiple Integrals.

Course Objectives:

The objective of this course is to make students able to:
  1. understand and formulate real-world problems into mathematical statements.
  2. develop solutions to mathematical problems at the level appropriate to the course.
  3. describe or demonstrate mathematical solutions either numerically or graphically.

Course Contents:


  1. Function of One Variable
    Teaching Hours : 5 hrs
    Four ways of representing a function, Linear mathematical model, Polynomial, Rational, Trigonometric, Exponential and Logarithmic functions, Combination of functions, Range and domain of functions and their Graphs

  2. Limits and Continuity
    Teaching Hours : 4 hrs
    Precise definition of Limit, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and Slant asymptotes

  3. Derivatives
    Teaching Hours : 4 hrs
    Tangents and velocity, Rate of change, Review of derivative, Differentiability of a function, Mean value theorem, Indeterminate forms and L’Hospital rule

  4. Applications of Derivatives
    Teaching Hours : 4 hrs
    Curve sketching, Review of maxima and minima of one variable, Optimization problems, Newton’s method

  5. Antiderivatives
    Teaching Hours : 5 hrs
    Review of antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite integral, The Fundamental theorem of calculus, Improper integrals

  6. Applications of Antiderivatives
    Teaching Hours : 5 hrs
    Areas between the curves, Volumes of cylindrical cells, Approximate Integrations, Arc length, Area of surface of revolution

  7. Ordinary Differential Equations
    Teaching Hours : 6 hrs
    Introduction, Introduction to first order equations Separable equations, Linear equations, Second order linear differential equations, Non homogeneous linear equations, Method of undetermined coefficients

  8. Infinite Sequence and Series
    Teaching Hours : 5 hrs
    Infinite sequence and series, Convergence tests and power series, Taylor’s and Maclaurin’s series

  9. Plane and Space Vectors
    Teaching Hours : 4 hrs
    Introduction, Applications, Dot product and cross Product, Equations of lines and Planes, Derivative and integrals of vector functions, Arc length and curvature, Normal and binormal vectors, Motion in space

  10. Partial Derivatives and Multiple Integrals
    Teaching Hours : 3 hrs
    Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values, Multiple integrals

Text Books:

  1. Calculus Early Transcendentals, James Stewart, 7E, CENGAGE Learning.

Reference Books:

  1. Calculus Early Transcendentals, Thomas, 12th Editions, Addision Wesley.

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