الجامعة :جامعة المنصورة |
الكلية :كلية العلوم |
القسم :الفيزياء |
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| 1- بيانات المقرر :- |
| | الرمز الكودى: | Phys613 | | اسم المقرر: | فيزياء رياضية (2) | | الفرقة: | درجة الماجستير فى العلوم / الفيزياء / الفيزياء النظرية | | عنوان البرنامج: | - جميع البرامج الاكاديمية
- الماجستير فى الفيزياء النظرية
| | التخصص: | رئيسياً | | عدد الساعات: | نظري: | 2 | فصل: | 1 | عملى: | |
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| 2- أهداف المقرر :- |
| - to introduce Methods of Mathematical Physics
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| 3- نواتج التعلم المستهدفة للمقرر :- |
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| 4- محتويات المقرر :- |
| | م | الموضوع | الأسبوع |
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| 1 | 1 Introduction 11 1.1 What Do I Need To Know From Calculus? 11 1.1.1 Introduction 11 1.1.2 Trigonometric Functions 13 1.1.3 Hyperbolic Functions 16 1.1.4 Derivatives 18 1.1.5 Integrals 19 1.1.6 Geometric Series 27 1.1.7 The Binomial Expansion 30 1.2 What I Need From My Intro Physics Class? 36 1.3 Technology and Tables 37 1.4 Appendix: Dimensional Analysis 38 Problems 43 iv 2 Free Fall and Harmonic Oscillators 45 2.1 Free Fall and Terminal Velocity 45 2.2 First Order Differential Equations 48 2.2.1 Separable Equations 49 2.2.2 Linear First Order Equations 50 2.2.3 Terminal Velocity 52 2.3 The Simple Harmonic Oscillator 54 2.3.1 Mass-Spring Systems 54 2.3.2 The Simple Pendulum 55 2.4 Second Order Linear Differential Equations 56 2.4.1 Constant Coefficient Equations 57 2.5 LRC Circuits 61 2.5.1 Special Cases 62 2.6 Damped Oscillations 66 2.7 Forced Systems 67 2.7.1 Method of Undetermined Coefficients 68 2.7.2 Forced Oscillations 71 2.7.3 Cauchy-Euler Equations 72 2.7.4 Method of Variation of Parameters 76 2.8 Numerical Solutions of ODEs 79 2.9 Linear Systems 85 2.9.1 Coupled Oscillators 85 2.9.2 Planar Systems 87 2.9.3 Equilibrium Solutions and Nearby Behaviors 89 2.9.4 Polar Representation of Spirals 100 2.10 Appendix: The Nonlinear Pendulum 102 Problems 106 v 3 Linear Algebra 111 3.1 Vector Spaces 111 3.2 Linear Transformations 117 3.3 Matrices 119 3.4 Eigenvalue Problems 130 3.4.1 An Introduction to Coupled Systems 130 3.4.2 Example of an Eigenvalue Problem 132 3.4.3 Eigenvalue Problems - A Summary 135 3.5 Matrix Formulation of Planar Systems 136 3.5.1 Solving Constant Coefficient Systems in 2D 137 3.5.2 Examples of the Matrix Method 140 3.5.3 Planar Systems - Summary 144 3.6 Applications 145 3.6.1 Circuits 145 3.6.2 Love Affairs 146 3.6.3 Predator Prey Models 147 3.6.4 Mixture Problems 147 3.6.5 Chemical Kinetics 149 3.6.6 Epidemics 150 3.7 Rotations of Conics 151 3.8 Appendix: Diagonalization and Linear Systems 155 Problems 160 4 The Harmonics of Vibrating Strings 165 4.1 Harmonics and Vibrations 165 4.2 Boundary Value Problems 167 4.3 Partial Differential Equations 169 4.4 The 1D Heat Equation 170 4.5 The 1D Wave Equation 174 vi 4.6 Introduction to Fourier Series 176 4.7 Fourier Trigonometric Series 180 4.8 Fourier Series Over Other Intervals 187 4.8.1 Fourier Series on [a, b] 192 4.9 Sine and Cosine Series 194 4.10 Solution of the Heat Equation 199 4.11 Finite Length Strings 201 4.12 Appendix: The Gibbs Phenomenon 203 Problems 208 5 Non-sinusoidal Harmonics and Special Functions 211 5.1 Function Spaces 212 5.2 Classical Orthogonal Polynomials 215 5.3 Fourier-Legendre Series 219 5.4 Gamma Function 230 5.5 Fourier-Bessel Series 232 5.6 Sturm-Liouville Eigenvalue Problems 237 5.6.1 Sturm-Liouville Operators 237 5.6.2 Properties of Sturm-Liouville Eigenvalue Problems 241 5.6.3 Adjoint Operators 243 5.6.4 Lagrange’s and Green’s Identities 245 5.6.5 Orthogonality and Reality 246 5.6.6 The Rayleigh Quotient - optional 247 5.6.7 The Eigenfunction Expansion Method - optional 249 5.7 Appendix: The Least Squares Approximation 251 5.8 Appendix: The Fredholm Alternative Theorem 254 Problems 25 | 1-12 |
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| 5- أساليب التعليم والتعلم :- |
| | م | الاسلوب |
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| 5 - Teaching and Learning Methods 5.1 - Lectures using board. 5.2 - Discussion sessions 5.3 - Problem classes 5.4 - class activity |
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| 6- أساليب التعليم والتعلم للطلاب ذوى القدرات المحدودة :- |
| - 1. Giving them more chance through the office hours to raise their competencies 2. class activity
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| 7- تقويم الطلاب :- |
| أ- التوقيت |
| | م | الطريقة | الأسبوع |
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| 1 | final exam | 12 | | 2 | med term exam | 6 | | 3 | oral exam | 12 |
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| ب- توزيع الدرجات |
| | م | الطريقة | الدرجة |
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| 1 | final exam | 80 | | 2 | med term exam | 10 | | 3 | oral exam | 10 | | المجموع | 100% |
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| 8- قائمة الكتب الدراسية والمراجع |
| | م | العنصر | النوع |
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| 1 | Mathematical physics | كتب ملزمة |
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| 9- مصفوفة المعارف والمهارات المستهدفة من المقرر الدراسي |
| | م | المحتوى | أسبوع الدراسة |
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| 1 Introduction 11 1.1 What Do I Need To Know From Calculus? 11 1.1.1 Introduction 11 1.1.2 Trigonometric Functions 13 1.1.3 Hyperbolic Functions 16 1.1.4 Derivatives 18 1.1.5 Integrals 19 1.1.6 Geometric Series 27 1.1.7 The Binomial Expansion 30 1.2 What I Need From My Intro Physics Class? 36 1.3 Technology and Tables 37 1.4 Appendix: Dimensional Analysis 38 Problems 43 iv 2 Free Fall and Harmonic Oscillators 45 2.1 Free Fall and Terminal Velocity 45 2.2 First Order Differential Equations 48 2.2.1 Separable Equations 49 2.2.2 Linear First Order Equations 50 2.2.3 Terminal Velocity 52 2.3 The Simple Harmonic Oscillator 54 2.3.1 Mass-Spring Systems 54 2.3.2 The Simple Pendulum 55 2.4 Second Order Linear Differential Equations 56 2.4.1 Constant Coefficient Equations 57 2.5 LRC Circuits 61 2.5.1 Special Cases 62 2.6 Damped Oscillations 66 2.7 Forced Systems 67 2.7.1 Method of Undetermined Coefficients 68 2.7.2 Forced Oscillations 71 2.7.3 Cauchy-Euler Equations 72 2.7.4 Method of Variation of Parameters 76 2.8 Numerical Solutions of ODEs 79 2.9 Linear Systems 85 2.9.1 Coupled Oscillators 85 2.9.2 Planar Systems 87 2.9.3 Equilibrium Solutions and Nearby Behaviors 89 2.9.4 Polar Representation of Spirals 100 2.10 Appendix: The Nonlinear Pendulum 102 Problems 106 v 3 Linear Algebra 111 3.1 Vector Spaces 111 3.2 Linear Transformations 117 3.3 Matrices 119 3.4 Eigenvalue Problems 130 3.4.1 An Introduction to Coupled Systems 130 3.4.2 Example of an Eigenvalue Problem 132 3.4.3 Eigenvalue Problems - A Summary 135 3.5 Matrix Formulation of Planar Systems 136 3.5.1 Solving Constant Coefficient Systems in 2D 137 3.5.2 Examples of the Matrix Method 140 3.5.3 Planar Systems - Summary 144 3.6 Applications 145 3.6.1 Circuits 145 3.6.2 Love Affairs 146 3.6.3 Predator Prey Models 147 3.6.4 Mixture Problems 147 3.6.5 Chemical Kinetics 149 3.6.6 Epidemics 150 3.7 Rotations of Conics 151 3.8 Appendix: Diagonalization and Linear Systems 155 Problems 160 4 The Harmonics of Vibrating Strings 165 4.1 Harmonics and Vibrations 165 4.2 Boundary Value Problems 167 4.3 Partial Differential Equations 169 4.4 The 1D Heat Equation 170 4.5 The 1D Wave Equation 174 vi 4.6 Introduction to Fourier Series 176 4.7 Fourier Trigonometric Series 180 4.8 Fourier Series Over Other Intervals 187 4.8.1 Fourier Series on [a, b] 192 4.9 Sine and Cosine Series 194 4.10 Solution of the Heat Equation 199 4.11 Finite Length Strings 201 4.12 Appendix: The Gibbs Phenomenon 203 Problems 208 5 Non-sinusoidal Harmonics and Special Functions 211 5.1 Function Spaces 212 5.2 Classical Orthogonal Polynomials 215 5.3 Fourier-Legendre Series 219 5.4 Gamma Function 230 5.5 Fourier-Bessel Series 232 5.6 Sturm-Liouville Eigenvalue Problems 237 5.6.1 Sturm-Liouville Operators 237 5.6.2 Properties of Sturm-Liouville Eigenvalue Problems 241 5.6.3 Adjoint Operators 243 5.6.4 Lagrange’s and Green’s Identities 245 5.6.5 Orthogonality and Reality 246 5.6.6 The Rayleigh Quotient - optional 247 5.6.7 The Eigenfunction Expansion Method - optional 249 5.7 Appendix: The Least Squares Approximation 251 5.8 Appendix: The Fredholm Alternative Theorem 254 Problems 25 | 1-12 |
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| اساتذة المادة: - |
| - السيد عبد العاطى حسن الوكيل
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| رئيس مجلس القسم العلمى: - |
| عادل محمد صادق عجور |
