First Semester
Mathematics
Course Description: This course covers the concepts of functions, limit, continuity, differentiation, integration of function of one variable; logarithmic, exponential, applications of derivatives and antiderivatives, differential equations, vector and applications, partial derivatives and multiple integration.
Course Objectives: The objective of this course is to make student able to understand and formulate real world problems into mathematical statements, develop solutions to mathematical problems at the level appropriate to the course and describe mathematical solutions either numerically or graphically.
Contents of Chapter |
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Unit 1: Function of One Variable (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 |
Unit 2: Limits and Continuity (4 Hrs.)Precise definition of Limit, Limits at infinity, Continuity, Horizontal asymptotes, Vertical and Slant asymptotes |
Unit 3: Derivatives (4 Hrs.)Tangents and velocity, Rate of change, Review of derivative, Differentiability of a function, Mean value theorem, Indeterminate forms and L’Hospital rule |
Unit 4: Applications of Derivatives (4 Hrs.)Curve sketching, Review of maxima and minima of one variable, Optimization problems, Newton’s method |
Unit 5: Antiderivatives (5 Hrs.)Review of antiderivatives, Rectilinear motion, Indefinite integrals and Net change, Definite integral, The Fundamental theorem of calculus, Improper integrals |
Unit 6: Applications of Antiderivatives (5 Hrs.)Infinite sequence and series, Convergence tests and power series, Taylor’s and Maclaurin’s series |
Unit 7: Ordinary Differential Equations (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 |
Unit 8: Infinite Sequence and Series (5 Hrs.)Infinite sequence and series, Convergence tests and power series, Taylor’s and Maclaurin’s series |
Unit 9: Plane and Space Vectors (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 |
Unit 10: Partial Derivatives and Multiple Integrals (3 Hrs.)Limit and continuity, Partial derivatives, Tangent planes, Maximum and minimum values, Multiple integrals |