# 2nd Year Course Outline

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Mathe Math 366 Course title: Calculus of FunctioCourse code: Math 366 Course category: compulsory Course outline Chapter 1. Vector valued functi 1.1 Definition and examples of vec1.2 Distance between two points, v1.3 Lines and planes in space 1.4 Introduction to vector-valued f 1.5 Calculus of vector-valued func 1.6 Change of parameter; arc lengt1.7 Unit, tangent, normal 1.8 Curvature Chapter 2 Limit and continuity of function 2.1 . Definitions and examples of re 2.2 Domain and range of functions2.3 Graphs and level curves 2.4 Limit and continuity Chapter 3 Differentiation of functions 3.1 Partial derivatives and its geom 3.2 Differentiability of functions of 3.3 The Chain rule atics   course outline     for Second year st semester ns of Several Variables ns or in space ectors algebra(dot product, projections, cross produnctions ions h function of several variables al valued functions of several variables of several variables functions of several variables etrical interpretation several variables miliyon@ymail.com tudents   ct)   miliyon@ymail.com 3.4 Implicit differentiation Chapter 4. Application of partial derivatives 4.1 Directional derivatives and gradient of functions of several variables 4.2 Tangent planes 4.3 Differentials and tangent plane approximations 4.4 Extreme values 4.5 Lagrange’s multiplier 4.6 Taylor’s theorem Chapter 5 Multiple integrals 5.1 Double integrals 5.2 Double integrals in polar coordinates 5.3 Surface area 5.4 Triple integrals 5.5 Triple integrals in cylindrical and spherical coordinates 5.6 Change of variables in multiple integrals Chapter 6. Calculus of vector field 6.1 Vector field 6.2 The divergence and curl of a vector field 6.3 Line integrals 6.4 Green’s theorem Textbook: - Robert Ellis and Denny Gulick, Calculus with analytic geometry , 5th References: - Leithold, The calculus with analytic geometry , 3rd Edition, Herper & Row, publishers . - R  . T . Smith and R. B. Minton, Calculus concepts and connections , McGram-Hill book company, 2006 - D. V . Widder, Advanced calculus , Prentice-Hall, 1979 - Ross L. Finney et al, Calculus , Addison Wesley, 1995 - E. J. Purcell and D. Varberg, Calculus with analytic geometry , Prentice-Hall INC., 1987 - Adams, Calculus: A complete course , 5th ed, Addison Wesley, 2003 - R. Wrede and M . R  . Spiegel, Theory of advanced calculus , 2nd ed., McGraw-Hill, - A. E . Taylor and W. R. Mann, Advanced calculus , 3rd ed, John-Wiley   miliyon@ymail.com Math 325 Course title: Linear Algebra I Course code: Math 325 Course category: compulsory Course outline Chapter 1: Vectors ( 2 hrs) 1.1 Definition of points in n-space 1.2 Vectors in n-space; geometric interpretation in 2 and 3-spaces 1.3 Scalar product, and norm of a vector, orthogonal projection, and direction cosines 1.4 The vector product 1.5 Applications on area and volume 1.6 Lines and planes Chapter 2: Vector spaces (9 hrs) 2.1 The axioms of a vector space 2.2 Examples of different models of a vector space 2.3 Subspaces, linear combinations and generators 2.4 Linear dependence and independence of vectors 2.5 Bases and dimension of a vector space 2.6 Direct sum and direct product of subspaces Chapter 3: Matrices ( 0 hrs) 3.1 Definition of a matrix 3.2 Algebra of matrices 3.3 Types of matrices: square, identity, scalar, diagonal, triangular, symmetric, and skew symmetric matrices 3.4 Elementary row and column operations 3.5 Row reduced echelon form of a matrix 3.6 Rank of a matrix using elementary row/column operations 3.7 System of linear equations Chapter 4: Determinants ( 2 hrs) 4.1 Definition of a determinant   miliyon@ymail.com 4.2 Properties of determents 4.3 Adjoint and inverse of a matrix 4.4 Cramer’s rule for solving system of linear equations (homogenous and non homogenous) 4.5 The rank of a matrix by subdeterminants 4.6 Determinant and volume 4.7 Eigenvalues and eigenvectors of a matrix 4.8 Diagonalization of a symmetric matrix Chapter 5: Linear Transformations (9 hrs) 5.1 Definition of linear transformations and examples 5.2 The rank and nullity of a linear transformation and examples 5.3 Algebra of linear transformations 5.4 Matrix representation of a linear transformation 5.5 Eigenvalues and eigenvectors of a linear transformation 5.6 Eigenspace of a linear transformation Teaching materials Textbooks: - Serge Lang; Linear Algebra Demissu Gemeda, An Introduction to Linear Algebra , Department of Mathematics, AAu, 2000 References: - D . C. Lay, Linear algebra and its applications , Pearson Addison Wesley, 2006 - Bernard Kolman & David R. Hill, Elementary linear algebra , 8th ed., Prentice Hall, 2004 - H . Anton and C Rorres, Elementary linear algebra , John Wiley & Sons, INC., 1994 - K. Hoffman & R. Kunze, Linear Algebra , 2nd ed., Prentice Hall INC . 1971   - S. Lipschutz, Theory and problems of linear algebra , 2nd ed . McGraw-Hill1991

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