Mathematics & Statistics
Texas Tech University
Kent Pearce

Department of Mathematics and Statistics
Texas Tech University
Lubbock, Texas 79409-1042
Voice: (806)742-2566 x 226
FAX: (806)742-1112
Email: kent.pearce@ttu.edu

Math 3350
Higher Mathematics for Engineers and Scientists
Spring 2010
Zill & Cullen
Advanced Engineering Mathematics
Jones & Bartlett

Review Exam I
Section Content      Suggested Problems
Section 1.1
  • definition of a differential equation
  • classification
    • type
    • order
    • linearity
  • notation: Leibnitz vs. Newton
  • definition of a solution of an ODE
  • explicit vs implicit solutions
  • family of solutions
    • one-parameter family of solutions
1-8
Section 1.2
  • initial-value problem (IVP)
  • first and second order IVP
  • existence and uniqueness
  • Theorem 1.1
2, 4, 7, 11,
Section 2.1
  • direction fields
 
Section 2.2
  • definition of a separable equation
  • method of solution
  • initial-value problem
5, 5, 7, 8, 10, 12, 18, 24-26
Section 2.3
  • definition of a linear equation
    • homogeneous
  • standard form of a linear equation
  • linearity property of solutions of the homogeneous equation
  • method of solution
    • find integrating factor exp(int(p(x)dx))
    • integrate the product of the integrating factor and f(x)
    • formualte the general solution of the linear equation
  • initial-value problem
  • functions defined by integration
3, 5, 7, 10-12, 14, 16, 18, 25, 26, 29
Section 2.4
  • definition of an exact equation
    • M(x,y)dx + N(x,y)dy = 0
  • criterion for being exact
  • method of solution
  • initial value problem
  • integrating factors
2-5, 7-9, 11, 14, 16, 19, 21, 23
Section 2.5
  • homogeneous functions
    • degree
  • homogenous first-order ODE
  • method of solution
    • substitution y = ux
    • substitution x = vy
  • Bernoulli equations
  • method of solution
    • u=y1-n
  • reduction to separable
    • substitution u = Ax + By + C
3-4, 6-7, 10-12, 15-16, 21, 23-24, 27-28
Section 2.6
  • tangent line approximation
  • slope from the direction field
  • Euler's Method
    • yn+1 = yn + h f(xn,yn)
  • error estimates
  • numerical solvers
None
Section 2.7
  • growth/decay linear models
    • dP/dt = kP
    • half-life
  • Newton's Law of Cooling/Heating
    • dT/dt = k(T-Tm)
    • ambient temperature
  • Mixtures
    • dx/dt = (input rate of salt) - (output rate of salt)
    • inflow volume equals outflow volume
    • inflow volume does not equal the outflow volume
3, 5, 11, 14-15, 21, 25
Section 2.8
  • population dynamics
  • logistic equation
  • solution of logistic equation
  • modifications of the logistic equation
None





Navigation Bar Home Vita Pre-Prints Courses Pre Lims Links Jokes

Home | Vita | Pre-Prints | Courses | Pre Lims | Links | Jokes

Comments maybe be mailed to: kent.pearce@ttu.edu

Last modified on: Monday, 10-Aug-2015 12:47:29 CDT