# 21MAT21: Advanced Calculus and Numerical Methods syllabus Physics Group 2021 Scheme

Advanced Calculus and Numerical Methods detailed syllabus for Physics Group 2021 Scheme curriculum has been taken from the VTUs official website and presented for the Physics Group students. For course code, course name, duration, number of credits for a course and other scheme related information, do visit full semester subjects post given below.

For Physics Group 2nd Sem scheme and its subjects, do visit Physics Group 2nd Sem 2021 Scheme scheme. The detailed syllabus of advanced calculus and numerical methods is as follows.

#### Teaching-Learning Process (General Instructions):

These are sample Strategies, which teacher can use to accelerate the attainment of the various course outcomes.

1. In addition to the traditional lecture method, different type of innovative teaching methods may be adopted so that the delivered lessons shall develop student’s theoretical and applied mathematical skills.
2. State the need for Mathematics with Engineering Studies and Provide real-life examples
3. Support and guide the students for self-study.
4. You will also be responsible for assigning homework, grading assignments and quizzes, and documenting students’ progress
5. Encourage the students for group learning to improve their creative and analytical skills
6. Show short related video lectures in following ways:
• As an introduction to new topics (pre-lecture activity).
• As a revision of topics (post-lecture activity).
• As additional examples (post-lecture activity).
• As an additional material of challenging topics (pre and post lecture activity).
• As a model solution of some exercises (post-lecture activity)

#### Module 1:

Integral Calculus Multiple Integrals: Evaluation of double and triple integrals, evaluation of double integrals by change of order of integration, changing into polar coordinates. Applications to find: Area and Volume by double integral. Problems. Beta and Gamma functions: Definitions, properties, relation between Beta and Gamma functions. Problems.
Self-Study: Center of gravity. (RBT Levels: L1, L2 and L3)

Teaching-Learning Process Chalk and Talk Method / Power Point Presentation

#### Module 2:

Vector Calculus Vector Differentiation: Scalar and vector fields. Gradient, directional derivative, curl and divergence – physical interpretation, solenoidal and irrotational vector fields. Problems. Vector Integration: Line integrals, Surface integrals. Applications to work done by a force and flux. Statement of Green’s theorem and Stoke’s theorem. Problems.
Self-Study: Volume integral and Gauss divergence theorem. (RBT Levels: L1, L2 and L3)

Teaching-Learning Process Chalk and Talk Method / Power Point Presentation

#### Module 4:

Numerical methods -1 Solution of polynomial and transcendental equations: Regula-Falsi and Newton-Raphson methods (only formulae). Problems. Finite differences, Interpolation using Newton’s forward and backward difference formulae, Newton’s divided difference formula and Lagrange’s interpolation formula (All formulae without proof). Problems. Numerical integration: Simpson’s (1/3)rd and (3/8)th rules(without proof). Problems. Self-Study: Bisection method, Lagrange’s inverse Interpolation, Weddle’s rule. (RBT Levels: L1, L2 and L3)

Teaching-Learning Process Chalk and Talk Method / Power Point Presentation

#### Module 5:

Numerical methods -2 Numerical Solution of Ordinary Differential Equations (ODE’s): Numerical solution of ordinary differential equations of first order and first degree: Taylor’s series method, Modified Euler’s method, Runge-Kutta method of fourth order, Milne’s predictor-corrector formula (No derivations of formulae). Problems. Self-Study: Adam-Bashforth method. (RBT Levels: L1, L2 and L3)

Teaching-Learning Process Chalk and Talk Method/Power Point Presentation

#### Course Outcomes:

(Course Skills Set) After successfully completing the course, the student will be able to understand the topics:

• Apply the concept of change of order of integration and change of variables to evaluate multiple integrals and their usage in computing the area and volume.
• Illustrate the applications of multivariate calculus to understand the solenoidal and irrotational vectors and also exhibit the inter dependence of line, surface and volume integrals.
• Formulate physical problems to partial differential equations and to obtain solution for standard practical PDE’s.
• Apply the knowledge of numerical methods in modelling of various physical and engineering phenomena.
• Solve first order ordinary differential equations arising in engineering problems.

#### Reference Books:

1. V. Ramana: “Higher Engineering Mathematics” McGraw-Hill Education, 11th Ed.
2. Srimanta Pal & Subodh C. Bhunia: “Engineering Mathematics” Oxford University press, 3rd Reprint, 2016.
3. N.P Bali and Manish Goyal: “A text book of Engineering Mathematics” Laxmi Publications, Latest edition
4. C. Ray Wylie, Louis C. Barrett: “Advanced Engineering Mathematics” McGraw – Hill Book Co. Newyork, Latest ed.
5. Gupta C.B, Sing S.R and Mukesh kumar: “Engineering Mathematics for Semester I and II”, Mc-Graw Hill Education(India) Pvt.Ltd. 2015
6. H.K.Dass and Er. Rajnish Verma: “Higher Engineering Mathematics” S. Chand Publication (2014).
7. James Stewart: “Calculus” Cengage publications, 7th edition, 4th Reprint 2019.

#### Web links and Video Lectures (e-Resources):

• http://.ac.in/courses.php?disciplineID=111
• http://www.class-central.com/subject/math(MOOCs)