### Calculus & Linear Algebra (18MAT11)

### CALCULUS & LINEAR ALGEBRA

### CLASS NOTES

**MODULE 1: DIFFERENTIAL CALCULUS-I**

**Lecture 1: Review of Differential Calculus**

**Lecture 2: Angle between the Radius vector & Tangent, Length of the perpendicular from the pole to the tangent**

**Lecture 3: Angle between the two polar curves - Problems**

**Lecture 4: Pedal equation of a polar curve - Problems**

**Lecture 5: Curvature & Radius of Curvature - Problems on Cartesian curve**

**Lecture 6: Curvature & Radius of Curvature - Problems on Polar curve**

**Lecture 7: Centre of Curvature and Circle of Curvature**

**Lecture 8: Introduction to Evolutes and Involutes**

**Lecture 9: Applications of Evolutes and Involutes**

**MODULE 2: DIFFERENTIAL CALCULUS-II**

**Lecture 1: Introduction to Taylor's and Maclaurin's series - Problems**

**Lecture 2: Problems on Taylor's and Maclaurin's series**

**Lecture 3: Indeterminate forms - L'Hospital rule**

**Lecture 4: Introduction to Partial Differentiation - Problems**

**Lecture 5: Total derivative - Chain rule - Problems**

**Lecture 6: Maxima & Minima for a function of two variables**

**Lecture 7: Lagrange's Method of Multipliers**

**Lecture 8: Applications to Maxima & Minima**

**Lecture 9: Jacobians**

**MODULE 3: INTEGRAL CALCULUS**

**VTU Important Questions**

**Lecture 1: Review of Integral Calculus**

**Lecture 2: Evaluation of Multiple Integrals**

**Lecture 3: Evaluation of Double Integrals over the region**

**Lecture 4: Changing the Order of Integration**

**Lecture 5: Changing into Polar Coordinates**

**Lecture 6: Applications of Multiple Integrals**

**Lecture 7: Beta & Gamma functions - Properties**

**Lecture 8: Problems on Gamma function**

**Lecture 9: Problems on Beta functions**

**MODULE 4: DIFFERENTIAL EQUATIONS**

**VTU Important Questions**

**Lecture 1: Exact - Reducible to Exact D.E. - Problems**

**Lecture 2: Bernoulli's Differential Equations**

**Lecture 3: Applications - Orthogonal Trajectories**

**Lecture 4: Applications - Newton's Law of Cooling **

**Lecture 5: Applications - Electrical Circuits**

**Lecture 6: Nonlinear Differential Equations**

**Lecture 7: Clairaut's Equation - Problems**

**Lecture 8: Reducible to Clairaut's equation**

**MODULE 5: LINEAR ALGEBRA**

**Lecture 1: Introduction to Linear Algebra**

**Lecture 2: Echelon form - Rank of a matrix.**

**Lecture 3: Some more problems on Rank of a matrix**

**Lecture 4: System of equations - consistency.**

**Lecture 5: Gauss Elimination - Gauss Jordan Methods**

**Lecture 6: Gauss Seidel Method - Problems**

**Lecture 7: Eigenvalues and Eigenvectors - Problems**

**Lecture 8: Rayleigh's Power Method**

**Lecture 9: Diagonalization of a square matrix **