Solution by Integrating Factors

Session Overview

In this session we will learn how to solve first order linear equations. We will apply the technique to solve the DE's for several different models.

Session Activities

Read the course notes:

• Solutions by Integrating Factors: Introduction (PDF)

Watch the lecture video clip:

• Solutions to Linear First Order ODE's (00:19:37)
• Transcript (PDF)

Read the course notes:

• Solutions to Linear First Order ODE's (PDF)
• Example: Heat Diffusion (PDF)

Check Yourself

Take the quizzes:

• The Meaning of k (PDF)
• Choices (PDF)
• Answer (PDF)


• Units (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Superposition and the Integrating Factors Solution (PDF)

Check Yourself

Take the quiz:

• Is It Particular? (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Watch the problem solving video:

• Solutions of First Order Linear Equations (00:08:55)
• Transcript (PDF)

Complete the practice problems:

• Practice Problems 5 (PDF)
• Practice Problems 5 Solutions (PDF)

Check Yourself

Complete the problem sets:

• Problem Set Part I Problems (PDF)
• Problem Set Part I Solutions (PDF)


• Problem Set Part II Problems (PDF)
• Problem Set Part II Solutions (PDF)

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First Order Linear ODE's

Session Overview

In this session we will start our study of linear equations, which is probably the most important class of differential equations. We will introduce the ideas and terminology of superposition, systems, input and response which will be used for the rest of the course.

Session Activities

Read the course notes:

• First Order Linear ODE's: Introduction (PDF)

Watch the lecture video clips:

• Linear First Order ODE's: Definition (00:07:26)
• Transcript (PDF)
• Linear First Order ODE's: Examples (00:15:47)
• Transcript (PDF)

Read the course notes:

• Linear First Order ODE's: Definition and Examples (PDF)

Check Yourself

Take the quizzes:

• Is It Linear? (PDF)
• Choices (PDF)
• Answer (PDF)


• Interpret the Graph (PDF)
• Choices (PDF)
• Answer (PDF)

Session Activities

Read the course notes:

• Systems: Input and Response (PDF)
• Superposition Principle (PDF)

Watch the problem solving video:

• Linear Equations (00:10:41)
• Transcript (PDF)

Complete the practice problems:

• Practice Problems 4 (PDF)
• Practice Problems 4 Solutions (PDF)

« Previous | Next »

Readings

Lectures 7-8

• Asymptotic notation: Section 3 from the Spring 2005 6.042 lecture notes on OCW (PDF)
• Order of growth: Sections 2.1 and 2.2 from Computational Modeling and Complexity Science
• Binary search: Wikipedia article on binary search (focus on the recursive implementation in Section 4)

Lectures 9-10

• Selection sort: Wikipedia article on selection sort
• Insertion sort: Wikipedia article on insertion sort
• Merge sort: Wikipedia article on merge sort

Readings

Lecture 4

• Functions, type conversion, and stack diagrams: Chapter 3 of How to Think Like a Computer Scientist
• More about functions: Chapter 5 of How to Think Like a Computer Scientist (through section 5.4)
• Recursion: Chapter 4 of How to Think Like a Computer Scientist (from section 4.9 on), as well as Chapter 5 of How to Think Like a Computer Scientist (from section 5.5 on)

Lecture 5

• Numbers: Floating point arithmetic: issues and limitations from the Python Tutorial
• Successive approximation: Wikipedia article on Newton's method

Lecture 6

• Lists: Chapter 8 of How to Think Like a Computer Scientist
• Dictionaries: Chapter 10 of How to Think Like a Computer Scientist
• As a reference: the Python Tutorial section on lists and dictionaries (feel free to skip 5.1.3 and 5.1.4)

Readings

Lectures 1-3

• Introduction: Chapter 1 of How to Think Like a Computer Scientist
• Variables and statements: Chapter 2 of How to Think Like a Computer Scientist
• Strings: Variables and strings section of Python Programming (also, the strings section)
• Python variables are names: Other languages have "variables", from Code Like A Pythonista: Idiomatic Python
• For PS0: Input/output section of Python Programming
• Conditionals: Chapter 4 of How to Think Like a Computer Scientist (through section 4.8), and the conditional statements section of Python Programming
• Iteration: Loops section of Python Programming
• Tuples: Tuples and sequences section of the Python Tutorial
• More on traversing and slicing strings: Chapter 7 of How to Think Like a Computer Scientist

MIT

6-00-introduction-to-computer-science-and-programming-fall-2008 http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-00-introduction-to-computer-science-and-programming-fall-2008/video-lectures/ readings 1: Introduction and Goals; Data Types, Operators, and Variables 2: Branching, Conditionals, and Iteration 3: Common Code Patterns: Iterative Programs 4: Abstraction through Functions; Introduction to Recursion 5: Floating Point Numbers, Successive Refinement, Finding Roots 6: Bisection Methods, Newton/Raphson, Introduction to Lists 7: Lists and Mutability, Dictionaries, Introduction to Efficiency 8: Complexity: Log, Linear, Quadratic, Exponential Algorithms 9: Binary Search, Bubble and Selection Sorts 10: Divide and Conquer Methods, Merge Sort, Exceptions 11: Testing and Debugging 12: Debugging, Knapsack Problem, Introduction to Dynamic Programming 13: Dynamic Programming: Overlapping Subproblems, Optimal Substructure 14: Introduction to Object-oriented Programming 15: Abstract Data Types, Classes and Methods 16: Encapsulation, Inheritance, Shadowing 17: Computational Models: Random Walk Simulation 18: Presenting Simulation Results, Pylab, Plotting 19: Biased Random Walks, Distributions 20: Monte Carlo Simulations, Estimating pi 21: Validating Simulation Results, Curve Fitting, Linear Regression 22: Normal, Uniform, and Exponential Distributions 23: Stock Market Simulation 24: Course Overview; What Do Computer Scientists Do?