Math 158: Basic Calculus II    -  Catalog Information 
Prerequisites: MATH 157 

Frequency: Fall/Spring Terms 

Credit: (3-2) 4 

Content: Infinite series, power series, Taylor series. Vectors, lines and planes in space. Functions of several variables: Limit,  continuity, partial derivatives, the chain rule, directional derivatives, tangent plane approximation and differentials, extreme values,  Lagrange multipliers. Double and triple integrals with applications. The line integral.  

Goals: Calculus was first discovered to meet the needs of the scientists of the sixteenth and seventeenth centuries. Diferential   calculus deals with the problem of calculating rates of change. It enables us to define slope of curves, to calculate velocities,   accelerations of moving bodies and to predict the times when planets would be closest together or farthest apart. Integral calculus  deals with the problem of determining a function from information about its rate of change. It enables us to calculate the future   location of a body from its present position, to find the areas of irregular regions in the plane, to measure the lengths of curves, and   to find the volumes and masses of arbitrary solids. The goal of this course is to present a modern view of calculus enhanced by the   use of technology. 
 

Course Outline: 

  •   (Week 2) Sequences and convergence of infinite series. Convergence tests.  
  •   (Week 2) Alternating series. Power series. Taylor and Binomial series.  
  •   (Week 1) Coordinates and vectors in space.Vector products. Lines and planes  
  •   (Week 1) Tangents and Normals.  
  •   (1 Week) Functions of several variables. Limits and continuity  
  •   (Week 1) Partial derivatives.The chain rule. The directional derivative  
  •   (Week 1) Extreme values. Lagrange Multipliers.  
  •   (Week 1) Double integrals.  
  •   (Week 2) Triple integral in cartesian, cylindrical and spherical coordinates.  
  •   (Week 1) Review  
Suggested textbook:
  • G.B. Thomas and R.Finney; Calculus and Analytic Geometry. Addison-Wesley Publishing Com. 1996.  
  • R.Ellis and D. Gulick; Calculus with Analytic Geometry, 5 th Edition, SCP, 1994  
  • M.Spivak; Calculus 3 rd Edition, Publish of Perish, Inc.  

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