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Dr. Abdelrahim Mousa
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Master Courses in Mathematics
MATH 739: Stochastic Differential Equations
MATH 860: Master Thesis Supervision
MATH 830: Master Seminar
Undergraduate Courses in Mathematics
MATH 411: Seminar in Mathematics
MATH 331: Ordinary Differential Equations
Math 330: Numerical Methods Using Matlab
MATH 234: Introduction to Linear Algebra
MATH 141: Calculus And Analytical Geometry I
MATH 132: Calculus And Analytical Geometry II
MATH 231: Calculus And Analytical Geometry III
MATH 1431: Calculus for Biology and Medicine
MATH 1351: Precalculus
MATH 2351: Calculus for Business and Economics
Undergraduate Courses in Applied Mathematics
MAEC 411: Seminar in Applied Mathematics
MAEC 333: General Equilibrium and Public Choice
MAEC 436: Game Theory
STAT 2311: Statistics I
STAT 236: Basic Statistics For Business Students
Undergraduate Courses in Leadership & Entrepreneurship
LRNJ201: Citizenship - Leadership and Civic Engagement
LRNJ301: Social Entrepreneurship 1 & 2
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MATH 1411: Calculus I
Text Book: Weir, Hass and Giordano. Thomas’ Calculus. 12th Edition
Discussion Problems Playlist 2020
Contents
1.1 Functions and their Graphs
1.2 Combining Functions
1.3 Trigonometric Functions
2.1 and 2.2 Rates of Change and Tangent to Curves and Limit of Functions
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits
2.5 Continuity
2.6 Limits Involving Infinity and Asymptotes of Graphs
3.1 Tangents and the Derivative at a Point
3.2 The Derivative as a Function
3.3 Differentiation Rules
3.4 The Derivative as a rate of Change
3.5 Derivatives of Trigonometric Functions
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Related Rates
3.9 Linearization and Differentials
4.1 Extreme Values of Functions
4.2 Mean Value Theorem
4.3 Monotonic Functions and the First derivative Test
4.4 Concavity and Curve Sketching
4.5 Applied Optimization
4.7 Anti Derivatives
5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Method
5.6 Substitution and Area Between Curves
6.1 Volumes Using Cross-Sections
6.2 Volumes Using Cylindrical Shells
6.3 Arc Length
6.4 Areas of Surfaces of Revolution
7.1 Inverse Functions and Their Derivatives
7.2 Natural Logarithms
7.3 Exponential Functions
7.4 Exponential Change and Separable Differential Equations
7.5 Indeterminate Forms and L'Hopital's Rule
7.6 Inverse Trigonometric Functions
7.7 Hyperbolic Functions
7.8 Relative Rates of Growth
8.1 Integration by Parts
8.2 Trigonometric Integral
8.3 Trigonometric Substitutions
8.4 Integration of Rational Functions by Partial Fractions
8.7 Improper Integrals
A.7 Complex Numbers
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MATH 1321: Calculus II
Text Book: Weir, Hass and Giordano. Thomas’ Calculus. 12th Edition
Discussion Problems Playlist 2020
Contents
10.1 Sequences
10.2 Infinite Series
10.3 The Integral Test
10.4 Comparison Tests
10.5 The Ratio and Root Tests
10.6 Alternating Series Absolute and Conditional Convergence
10.7 Power Series
10.8 Taylor and Maclaurin Series
10.9 Convergence of Taylor Series
10.10 The Binomial Series and Applications of Taylor Series
11.1 Parametrizations of Plane Curves
11.2 Calculus with Parametric Curves
11.3 Polar Coordinates
11.4 Graphing in Polar Coordinates
11.5 Areas and Lengths in Polar Coordinates
11.6 Conic Sections
12.1 Three-Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Lines and Planes in Space
12.6 Cylinders and Quadratic Surfaces
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MATH 2311: Calculus III
Text Book: Weir, Hass and Giordano. Thomas’ Calculus. 12th Edition
Contents
13.1 Curves in Space and Their Tangents
13.2 Integrals of Vector Functions
13.3 Arc Length in Space
13.4 Curvature and Normal Vectors of a Curve
13.5 Tangential and Normal Components of Acceleration
14.1 Functions of Several Variables
14.2 Limits and Continuity in Higher Dimensions
14.3 Partial Derivatives
14.4 The Chain Rule
14.5 Directional Derivatives and Gradient Vectors
14.6 Tangent Planes and Differentials
14.7 Extreme Values and Saddle Points
14.8 Lagrange Multipliers
15.1 Double and Iterated Integrals over Rectangles
15.2 Double Integrals over General Regions
15.3 Area by Double Integration
15.4 Double Integrals in Polar Form
15.5 Triple Integrals in Rectangular Coordinates
15.6 Moment and Centers of Mass
15.7 Triple Integrals in Cylindrical and Spherical Coordinates
15.8 Substitution in Multiple Integrals
16.1 Line Integrals
16.2 Vector Fields and Line Integrals
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Math234: Linear Algebra with Applications
Text Book: Steven J. Leon. Linear Algebra with Applications. 9th Edition
Contents
1.1 Systems of Linear Equations
1.2 Row Echelon Form
1.3 Matrix Arithmetic
1.4 Matrix Algebra
1.5 Elementary Matrices
2.1 The Determinant of a Matrix
2.2 Properties of Determinants
2.3 The Adjoint of a Matrix
3.1 Vector Spaces - Definition and Examples
3.2 Subspaces
3.3 Linear Independence
3.4 Basis and Dimension
3.5 Change of Basis
3.6 Row Space and Column Space
4.1 Linear Transformations - Definition and examples
4.2 Matrix Representations of Linear transformations
6.1 Eigenvalues and Eigenvectors
6.3 Diagonalization
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MATH 331: Ordinary Differential Equations
Text Book: Boyce and DiPrima.
Elementary Differential Equations and Boundary Value Problems . 9th Edition
Contents
1.1 Some Basic Mathematical Models and Direction Fields
1.2 Solutions of Some Differential Equations
1.3 Classification of Differential Equations
2.1 Linear Differential Equations and Method of Integrating Factors
2.2 Separable Differential Equations
2.3 Modeling with First Order Equations
2.4 Differences Between Linear and Nonlinear Differential Equations
2.5 Autonomous Differential Equations and Population Dynamics
2.6 Exact Differential Equations and Integrating Factors
2.7 Numerical Approximations and Euler Method
2.8 The Existence and Uniqueness Theorem
2.9 Solving some 2nd order Differential Equations
3.1 Homogeneous Equations with Constant Coefficients
3.2 Solutions of Linear Homogeneous Differential Equations; the Wronskian
3.3 Complex Roots of the Characteristic Equation
3.4 Repeated Roots; Reduction of Order Method
3.5 Nonhomogeneous Differential Equations; Method of Undetermined Coefficients
3.6 Variation of Parameters Method
4.1 General Theory of nth Order Linear Differential Equations
4.2 Homogeneous Differential Equations with Constant Coefficients
4.3 The Method of Undetermined Coefficients
4.4 The Method of Variation of Parameters for Higher Order Linear Differential Equations
5.1 Review of Power Series
5.2 Series Solutions Near an Ordinary Point I
5.3 Series Solutions Near an Ordinary Point II
5.4 Euler Differential Equations and Regular Singular Points
5.5 Series Solutions Near a Regular Singular Point I
6.1 Definition of the Laplace Transform
6.2 Solution of Initial Value Problems
6.3 Step Functions
6.4 Differential Equations with Discontinuous Forcing Functions
6.5 Impulse Functions
6.6 The Convolution Integral
7.5 Homogeneous Linear Systems with Constant Coefficients
7.6 Complex Eigenvalues
7.8 Repeated Eigenvalues
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MATH 330: Numerical Methods Using Matlab:
Text Book: John H. Mathews & Kurtis D. Fink.
Numerical Methods Using Matlab. Pearson Education Inc., 4th Edition, 2004
Contents
1.1 Review of Calculus
1.3 Error Analysis and Order of Approximation
2.1 Fixed Point Iteration and Upper Bound of Error
2.2 Bracketing Methods_Bisection Method
2.2 Bracketing Methods_False Position Method
2.4 Newton Raphson Method, Secant Method, Multiplicity of Roots, Speed of Convergence
Ch3 Cost of Solving Linear Systems
Ch3 Cost of Backward Substitutions
Ch3 Cost of Gaussian Elimination
Ch3 Cost of LU Factorization
Ch3 Cost of Cramer's Rule
Ch3 Cost of Gauss Jordan Reduction
Ch3 Cost of Inverse Method
Ch3 Solving Nonlinear Systems Using Newton Raphson Method
Ch3 Solving Nonlinear Systems Using Fixed Point Iteration
Ch3 Solving Nonlinear Systems Using Seidel Iteration
Ch4 Interpolation
Ch4 Lagrange Polynomial
Ch4 Newton Polynomial
Ch4 Error Terms and Error Bound
Ch5 Curve Fitting
Ch5 Least Squares
Ch5 Linearization
Ch5 Spline Functions
Ch6 Numerical Differentiation
Ch6 Difference Formulas
Ch6 Derivation of Difference Formulas
Ch6 Error Analysis and Optimal Step Size
Ch7 Numerical Integration
Ch7 The Degree of Precision
Ch7 Composite Trapezoidal Rule
Ch7 Composite Simpson Rule
Ch7 Gauss Legegendre Integration
Ch7 Gauss Legegendre Translation
Ch9 Numerical Approximation for IVPs
Ch9 Euler Method
Ch9 Taylor Method of Order 2
Ch9 Heun Method
Ch9 Rung Kutta
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Have a look to this video helping you how to install Matlab
Start Installing Matlab
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STAT 2361: Basic Statistics For Business Students:
Text Book: Dennis J. Sweeney, Thomas A. Williams And David R. Anderson.
Fundamentals of Business Statistics, Fifth Edition, 2009
Contents
1.1 - 1.2 Applications in Business and Economics
1.3 Data Sources
1.4 Descriptive Statistics
2.1 Tabular and Graphical Presentations
2.2 Summarizing Quantitative Data
2.3 The Stem and Leaf Display
2.4 Cross-Tabulations and Scatter Diagrams
3.1 Measures of Location
3.2 Measures of Variability
3.3 Measures of Distribution Shape
3.4 Exploratory Data Analysis
3.5 Measures of Association Between Two Variables
3.6 The Weighted Mean and Grouped Data
4.1 Experiments and Counting Rules
4.2 Events and their Probabilities
4.3 Some Basic Relationships of Probability
4.4 Conditional Probabilities
5.1 Random Variables
5.2 Discrete Probability Distribution
5.3 Expected Value and Variance
5.4 Binomial Probability Distribution
5.5 Poisson Probability Distribution
6.1 Uniform Probability Distribution
6.2 Normal Probability Distribution
6.3 Normal Approximation of Binomial Probabilities
6.4 Exponential Probability Distribution
7.1 Sampling
7.2 Selected a Sample
7.3 Point Estimation
7.4 Introduction to Sampling Distribution
7.5 Sampling Distribution of the Sample Mean
7.6 Sampling Distribution of the Sample Proportion
7.7 Sampling Methods
8.1 Population Mean when Sigma is Known
8.2 Population Mean when Sigma is Unknown
8.3 Determining the Sample Size
8.4 Population Proportion
9.1 Null and Alternative Hypothesis
9.2 Type I and II Errors
9.3 Hypothesis Testing about Population Mean when Sigma is Known
9.4 Hypothesis Testing about Population Mean when Sigma is Unknown
9.5 Hypothesis Testing about Proportion
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MATH 1351: Pre-Calculus
Text Book: Ronald Harshbarger and James Reynolds.
Mathematical Applications for the Management, Life and Social Sciences, Tenth Edition, 2013
Contents
0.1 Sets
0.2 The Real Numbers
0.3 Exponents
0.4 Radicals
0.5 Operations with Algebraic Expressions
0.6 Factoring
0.7 Algebraic Fractions
1.1 Solutions of Linear Equations and Inequalities
1.2 Functions
1.3 Linear Functions
1.5 Solutions of Systems of Linear Equations
2.1 Quadratic Equations: Quadratic Formula
2.2 Quadratic Functions: Parabolas
2.4 Special Functions and Their Graphs
3.1 Matrices
3.2 Multiplication of Matrices
3.4 Inverse of Square Matrix
4.1 Linear Inequalities in Two Variables
4.2 Linear Programming
5.1 Exponential Functions
5.2 Logarithmic Functions and Their Properties
5.3 Solution of Exponential Equations
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MATH 2351: Calculus for Business and Economics
Text Book: Ronald Harshbarger and James Reynolds.
Mathematical Applications for the Management, Life and Social Sciences, Tenth Edition, 2013
Lecture Notes - تلخيص المادة 1
Lecture Notes - تلخيص المادة 2
Contents
1.2 Functions
1.3 Linear Functions
1.6 Applications of Functions in Business and Economics
2.1 Quadratic Equations: Quadratic Formula
2.2 Quadratic Functions: Parabolas
2.3 Business Applications Using Quadratics
5.1 Exponential Functions
5.2 Logarithmic Functions and Their Properties
5.3 Solution of Exponential Equations
6.1 Simple Interest and Sequences
6.2 Compound Interest - Geometric Sequences
9.1 Limits
9.2 Continuous functions, limits at infinity
9.3 Average and Instantaneous Rates of Change
9.4 Derivative Formulas
9.5 The Product Rule and the Quotient Rule
9.6 The chain rule and power rule
9.7 Using derivative formulas
9.8 High order derivatives
9.9 Applications of Derivatives in business and economics
10.1 Relative Maxima and Minima
10.2 Concavity: Points of inflection, Second Derivative test
10.3 Optimization in Business and Economics
11.1 Derivatives of Logarithmic Functions
11.2 Derivatives of Exponential Functions
11.3 Implicit Differentiation
11.5 Applications in Business and Economics
12.1 The Indefinite Integral
12.2 The Power Rule
12.3 Integrals Involving Exponential and Logarithmic Functions
12.4 Applications of the Indefinite Integral in Business and Economics
13.2 The Definite Integral: The Fundamental Theorem of Calculus
13.3 Area between two curves
13.4 Applications of Definite Integrals in Business and Economics
14.1 Functions of two variables
14.2 Partial Differentiation
14.3 Applications of Functions of Two Variables in Business and Economics
14.4 Maxima and Minima