Calculus I – APSC 171

Calendar Description: Graphs and derivatives of vector-valued functions; related applications. Implicit derivatives and related rate applications. Fundamental Theorem of Calculus, Riemann integral; applications to problems involving areas, volumes, mass, charge, work, etc. Integration by substitution, by parts, and partial fractions. Introduction to second-order differential equations and complex numbers.

Week 1 – Derivatives and Vectors

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions
  

Week 2 – Vector-Valued Functions

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 3 – Derivatives with Vector-Valued Functions

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 4 – Inverse Trig, Tangent Lines and Linearization

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 5 – Implicit Derivatives, Related Rates and Optimization

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 6 – Defining and Estimating Integrals as Areas

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 7 – The Fundamental Theorem of Calculus

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 8 – Integration by Parts and Substitution

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 9 – Integrals for Volume and Work; Partial Fractions

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 10 – Differential Equations and Complex Numbers 1

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 11 – Differential Equations and Complex Numbers 2

• Videos – YouTube playlist or Queen’s streaming server
• Notes for Videos – Incomplete (PDF), Complete (PDF)
• Practice Problems: Questions, Solutions

Week 12 – Review

No new material was presented in Week 12.