calculus .pdf

Course No: 1 Course Name: Calculus Course Code: BMAS 0110 Batch: Programme: Semester: L T P J Credits Contact Hrs. B. Tech. (CSE- AIML) I Year III/IV Per Week: 4 2024-2028...

Course No: 1 Course Name: Calculus Course Code: BMAS 0110 Batch: Programme: Semester: L T P J Credits Contact Hrs. B. Tech. (CSE- AIML) I Year III/IV Per Week: 4 2024-2028 3 1 0 0 4 Total Hours: 40 Total Evaluation Marks: 100 Examination Duration: Mid Term (2 hours), End Term (3 hours) Mid Term: 30 Marks End Term: 50 Marks Pre-requisite of course: NIL Internal Assessment: 20 Marks Course To make the students understand the concepts of calculus, ordinary differential equations and Objective difference equations by giving more emphasis to their applications in engineering fields. After studying these topics, the students will be able to: CO1: Understand partial differentiation and its applications Course CO2: Expand a real valued function of several variables in Taylor’s series Outcomes CO3: Calculate Jacobian and know its applications CO4: Use Lagrange’s method of multipliers in determining the extrema of functions CO5: Find gradient, divergence and curl of a field and know their applications CO6: Evaluate double & triple integrals and study their applications CO7: Apply numerical integration to solve definite integrals CO8: Solve ordinary differential equations of higher order CO9: Numerically solve the first order IVP by Runge-Kutta IV order method CO10: Solve a difference equation. COURSE SYLLABUS Module No. Content Hours [Course Outcome(s) No.: 1, 2, 3, 4 and 5] Differential Calculus: Introduction to partial Derivatives, Euler’s theorem for I homogeneous functions, Composite functions, Total derivatives, Expansion of function of several variables by Taylor’s series, Jacobian and its applications, Functional dependence, Extrema of functions of several variables, Lagrange’s method of 20 multipliers. Vector Calculus: Introduction, Scalar and vector point functions, Gradient of a scalar field, Directional derivative, divergence and curl of vector field, Physical interpretation of gradient, divergence and curl, Vector Identities, Applications. [Course Outcome(s) No.: 6, 7, 8, 9 and 10] Integral Calculus: Beta and Gamma functions, Double Integral, Change of order of II integration, Triple integral, Errors and their analysis, Types of error, Numerical integration by Trapezoidal and Simpson’s rules (without proof). Ordinary Differential Equations: Linear differential equation of nth order with 20 constant coefficients, Euler-Cauchy Equations, Simultaneous differential equations, Numerical solution of first order initial value problems by Runge-Kutta IV order method. Applications to Engineering problems. Difference Equation: Finite difference operators, relation between operators, Introduction to difference equation, Solution of difference equation, Complementary function and particular integral. Text Books:  Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2011.  M. K. Jain, S. R. K. Iyengar and R. K. Jain, Advanced Engineering Mathematics, Narosa Publishing House, New Delhi, 2002.  W. E. Boyce and R. D. Prima, Elementary Differential Equations, John Wiley & Sons, 2009.  B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi, 2014.  S. S. Sastry, Introductory Methods of Numerical Analysis, PHI, 2012. Reference Books:  T. M. Apostol, Calculus, Volume I, John Wiley & Sons, Inc., USA, 1967.  T. M. Apostol, Calculus, Volume II, Xerox Corporation, USA, 1969.  N. P. Bali and M. Goyal, A Text Book of Engineering Mathematics, Laxmi Publications, Delhi, 2014.  G. B. Thomas and R. Finney, Calculus and Analytic geometry, Addison Wesley, USA, 1995.