محتويات كتب في عالم الرياضيات

(1)

Calculus I (Math 2413)

 

المحتويات
  • Algebra/Trig Review – Trig Functions and Equations, Exponential Functions and Equations, Logarithm Functions and Equations.
  • Limits – Concepts, Definition, Computing, One-Sided Limits, Continuity, Limits Involving Infinity, L’Hospitals Rule
  • Derivatives – Definition, Interpretations, Derivative Formulas, Power Rule, Product Rule, Quotient Rule, Chain Rule, Higher Order Derivatives, Implicit Differentiation, Logarithmic Differentiation, Derivatives of Trig Functions, Exponential Functions, Logarithm Functions, Inverse Trig Functions, and Hyperbolic Trig Functions.
  • Applications of Derivatives – Related Rates, Critical Points, Minimum and Maximum Values, Increasing/Decreasing Functions, Inflection Points, Concavity, Optimization
  • Integration – Definition, Indefinite Integrals, Definite Integrals, Substitution Rule, Evaluating Definite Integrals, Fundamental Theorem of Calculus
  • Applications of Integrals – Average Function Value, Area Between Curves, Solids of Revolution, Work

(2)

Calculus I I Math 2414
المحتويات
Integration Techniques – Integration by Parts, Integrals Involving Trig Functions, Trig Substitutions, Integration using Partial Fractions, Integrals Involving Roots, Integrals Involving Quadratics, Integration Strategy, Improper Integrals, Comparison Test for Improper Integrals, and Approximating Definite Integrals.
Applications of Integrals – Arc Length, Surface Area, Center of Mass/Centroid, Hydrostatic Pressure and Force, Probability.
Parametric Equations and Polar Coordinates – Parametric Equations & Curves, Calculus with Parametric Equations (Tangents, Areas, Arc Length and Surface Area), Polar Coordinates, Calculus with Polar Coordinates (Tangents, Areas, Arc Length and Surface Area).
Sequences and Series – Sequences, Series, Convergence/Divergence of Series, Absolute Series, Integral Test, Comparison Test, Limit Comparison Test, Alternating Series Test, Ratio Test, Root Test, Estimating the Value of a Series, Power Series, Taylor Series, Binomial Series
Vectors – Basics, Magnitude, Unit Vector, Arithmetic, Dot Product, Cross Product, Projection
Three Dimensional Coordinate System – Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates

(3)
Calculus III Math 2415
المحتويات
Three Dimensional Coordinate System – Equations of Lines, Equations of Planes, Quadratic Surfaces, Functions of Multiple Variables, Vector Functions, Limits, Derivatives, and Integrals of Vector Functions, Tangent Vectors, Normal Vectors, Binormal Vectors, Curvature, Cylindrical Coordinates, Spherical Coordinates  

Partial Derivatives – Limits, Partial Derivatives, Higher Order Partial Derivatives, Differentials, Chain Rule, Directional Derivatives, Gradient.

Applications of Partial Derivatives – Tangent Plane, Normal Line, Relative Extrema, Absolute Extrema, Optimization, Lagrange Multipliers.

Multiple Integrals – Iterated Integrals, Double Integrals, Double Integrals in Polar Coordinates, Triple Integrals, Triple Integrals in Cylindrical Coordinates, Triple Integrals in Spherical Coordinates, Change of Variables, Surface Area.

Line Integrals – Vector Fields, Line Integrals With Respect to Arc Length, Line Integrals With Respect to x and y, Line Integrals of Vector Fields, Fundamental Theorem of Line Integrals, Conservative Vector Fields, Potential Functions, Green’s Theorem, Curl, Divergence.

Surface Integrals – Parametric Surfaces, Surface Integrals, Surface Integrals of Vector Fields, Stokes’ Theorem, Divergence Theorem

(4)

Algebra Math 1314

المحتويات
  • Preliminaries – Exponent Properties, Rational Exponents, Negative Exponents, Radicals, Polynomials, Factoring, Rational Expressions, Complex Numbers
  • Solving Equations and Inequalities – Linear Equations, Quadratic Equations, Completing the Square, Quadratic Formula, Applications of Linear and Quadratic Equations, Reducible to Quadratic Form, Equations with Radicals, Linear Inequalities, Polynomial & Rational Inequalities, Absolute Value Equations & Inequalities.
  • Graphing and Functions – Graphing Lines, Circles, and Piecewise Functions, Function Definition, Function Notation, Function Composition, Inverse Functions.
  • Common Graphs – Parabolas, Ellipses, Hyperbolas, Absolute Value, Square Root, Constant Function, Rational Functions, Shifts, Reflections, Symmetry.
  • Polynomial Functions – Dividing Polynomials, Zeroes/Roots of Polynomials, Finding Zeroes of Polynomials, Graphing Polynomials, Partial Fractions.
  • Exponential and Logarithm Functions – Exponential Functions, Logarithm Functions, Solving Exponential Functions, Solving Logarithm Functions, Applications.
  • (5)
  • Linear Algebra Math 2318
  • المحتويات 

     

    • Systems of Equations and Matrices – Systems of Equations, Row-Echelon Form, Reduced Row-Echelon Form, Gaussian Elimination, Gauss-Jordan Elimination, Matrices, Matrix Arithmetic, Transpose, Inverse Matrices, LU-Decompositions.
    • Determinants – The Determinant Function, Properties of Determinants, Method of Cofactors, Determinants by Row Reduction, Cramer’s Rule.
    • Euclidean n-space – Vectors, Vector Arithmetic, Norm, Dot Product, Cross Product, Projections, Euclidean n-space, Linear Transformations.
    • Vector Spaces – Vector Space Axioms, Examples of Vector Spaces, Subspaces, Span, Linear Independence, Linear Dependence, Basis, Dimension, Null Space, Row Space, Column Space, Inner Product Spaces, Orthogonal/Orthonormal Basis, Least Squares, QR-Decomposition, Orthogonal Matrices
    • Eigenvalues and Eigenvectors – Review of Determinants, Eigenvalues and Eigenvectors, Diagonalization

  • (6)
  • المعادلات التفاضلية
    Differential Equations
    المحتويات 

    First Order Differential Equations

    Linear Equations Identifying and solving linear first order differential equations.
    Separable Equations Identifying and solving separable first order differential equations. We’ll also start looking at finding the interval of validity from the solution to a differential equation.
    Exact Equations Identifying and solving exact differential equations. We’ll do a few more interval of validity problems here as well.
    Intervals of Validity Here we will give an in-depth look at intervals of validity as well as an answer to the existence and uniqueness question for first order differential equations.
    Modeling with First Order Differential Equations Using first order differential equations to model physical situations. The section will show some very real applications of first order differential equations.
    Equilibrium Solutions We will look at the behavior of equilibrium solutions and autonomous differential equations.

    Euler’s Method In this section we’ll take a brief look at a method for approximating solutions to differential
    equations

    المصدر : الجامعات السعودية, http://www.ksau.info/vb/showthread.php?t=9847
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