UNIT – I MATRICES Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications: Stretching of an elastic membrane. □ To acquaint the student with mathematical tools needed in evaluating multiple integrals and their applications. □ To make the students understand various techniques of integration. This is needed in many branches of engineering. □ To familiarize the student with functions of several variables. □ To familiarize the students with differential calculus. Matrix and Calculus Syllabus MA3151 pdf download free.ĬOURSE OBJECTIVES: □ To develop the use of matrix algebra techniques that is needed by engineers for practical applications. 14.5: The Chain Rule.9 14.6: Directional Derivatives and the Gradient Vector.8 14.7: Maximum and Minimum Values.1 14.8: Lagrange Multipliers.3 14: Review.3 Problems Plus.7 Ch 15: Multiple Integrals.9 15.1: Double Integrals over Rectangles.0 15.2: Double Integrals over General Regions.3 15.3: Double Integrals in Polar Coordinates.2 15.4: Applications of Double Integrals.8 15.5: Surface Area.8 15.6: Triple Integrals.1 15.7: Triple Integrals in Cylindrical Coordinates.2 15.8: Triple Integrals in Spherical Coordinates.7 15.9: Change of Variables in Multiple Integrals.4 15: Review.3 Problems Plus.7 Ch 16: Vector Calculus.9 16.1: Vector Fields.0 16.2: Line Integrals.7 16.3: The Fundamental Theorem for Line Integrals.9 16.4: Green's Theorem.8 16.5: Curl and Divergence.5 16.6: Parametric Surfaces and Their Areas.3 16.7: Surface Integrals.4 16.8: Stokes' Theorem.6 16.9: The Divergence Theorem.3 16.10: Summary.9 16: Review.0 Problems Plus.3 Ch 17: Second-Order Differential Equations.5 17.1: Second-Order Linear Equations.6 17.2: Nonhomogeneous Linear Equations.2 17.3: Applications of Second-Order Differential Equations.0 17.4: Series Solutions.8 17: Review.3 Appendixes.5 A: Numbers, Inequalities, and Absolute Values.6 B: Coordinate Geometry and Lines.4 C: Graphs of Second-Degree Equations.0 D: Trigonometry.8 E: Sigma Notation.8 F: Proofs of Theorems.3 G: Complex Numbers.2 H: Answers to Odd-Numbered Exercises.1 Index.5 Reference.7 Concept Check Answers.MA3151 Syllabus Matrix and Calculus Regulation 2021 Anna University free download. 14.4: Tangent Planes and Linear Approximations. 13.4: Motion in Space: Velocity and Acceleration. 13.2: Derivatives and Integrals of Vector Functions. 12.1: Three-Dimensional Coordinate Systems. Ch 12: Vectors and the Geometry of Space. 11.11: Applications of Taylor Polynomials. 11.9: Representations of Functions as Power Series. 11.6: Absolute Convergence and the Ratio and Root Tests. 11.3: The Integral Test and Estimates of Sums. 10.6: Conic Sections in Polar Coordinates. 10.4: Areas and Lengths in Polar Coordinates. 10.1: Curves Defined by Parametric Equations. Ch 10: Parametric Equations and Polar Coordinates. 9.2: Direction Fields and Euler's Method. 9.1: Modeling with Differential Equations. 8.4: Applications to Economics and Biology. 8.3: Applications to Physics and Engineering. Ch 8: Further Applications of Integration. 7.6: Integration Using Tables and Computer Algebra Systems. 7.4: Integration of Rational Functions by Partial Fractions. 6.8: Indeterminate Forms and l'Hospital's Rule. ![]() 6.4: Derivatives of Logarithmic Functions. 6.2: Exponential Functions and Their Derivatives. 4.4: Indefinite Integrals and the Net Change Theorem. 4.3: The Fundamental Theorem of Calculus. 3.6: Graphing with Calculus and Calculators. 3.4: Limits at Infinity Horizontal Asymptotes. 3.3: How Derivatives Affect the Shape of a Graph. 2.9: Linear Approximations and Differentials. 2.7: Rates of Change in the Natural and Social Sciences. 2.4: Derivatives of Trigonometric Functions. ![]() 1.6: Calculating Limits Using the Limit Laws. 1.2: Mathematical Models: A Catalog of Essential Functions. ![]() Calculators, Computers, and Other Graphing Devices.
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