MATH 230H, Honors Calculus and Vector Analysis
(three-dimensional analytic geometry; vectors in space; partial differentiation; double and triple integrals; integral vector calculus.)

Syllabus - Extra credit problems

• HWA-1, due Mon, Aug 29.
  • Exercises: 1.3.9, 1.3.22, 1.3.25, 1.3.26, 1.4.17.
  • Optional: Watch Vectors, what even are they?
• HWA-2, due Wed, Sep 7.
  • Exercises: 1.4.16, 1.4.23, 1.5.8, 1.5.14, 1.5.20.
• HWA-3, due Mon, Sep 12.
  • Exercises: 1.6.4, 1.6.10, 1.7.9, 1.7.13, 1.8.10.
• HWA-4, due Mon, Sep 19.
  • Exercises: 1.8.2, 1.8.11, 1.8.12, 1.9.2, 1.9,6.
• HWA-5, due Mon, Sep 26.
  • Assume that the trajectory of the back wheel of an ideal bicycle is given by smooth plane curve b(t), here t denotes time. Write an expression for the trajectory of the front wheel f(t). Show that the speed of the back wheel can not exceed the speed of the front wheel.
    We assume that in the ideal bicycle the distance from back wheel and front wheel is fixed, let us denote it by R and the back wheel always moves in the direction to the front wheel.
  • Exercises: 1.8.15, 1.9,4, 2.1.6, 2.1.10
• HWA-6, due Mon, Oct 3.
  • Exercises: 2.1.16, (2.2.14 and 2.2.25), 2.3.4, 2.4.4, 2.4.16.
• HWA-7, due Mon, Oct 10.
  • Exercises: 2.3.9, 2.4.21, 2.5.2. 2.5.13, 2.7.4.
• HWA-8, due Mon, Oct 17.
  • Exercises: 2.1.18, 2.5.4, 2.7.2, 2.7.5, 3.3.2.
• Midterm Thu, Oct 20.
  • In class, 5 problems;
• HWA-9, due Mon, Oct 24.
  • Evaluate \(\iint\limits_D xy\, dA\), where \(D\) is the intesection of the unit disc \(x^2+y^2\le 1\) and the positive quadrant \(x\ge 0,\ y\ge 0\).
  • Exercises: 2.1.20, 2.2.28, 3.3.4, 3.3.11.
• HWA-10, due Mon, Oct 31.
  • Exercises: 3.5.2, 3.5.6, 3.5.9, 3.5.10, 3.6.10
• HWA-11, due Mon, Nov 7.
  • Assume the plane region \(R\) is defined by the inequalities \(x\le 2y\le 4x\le 1\). Rewrite double integral \(\iint\limits_{R} f(x,y)\,dA,\) as an iterated integral.
  • Find the volume of the intersection of two balls defined by the inequalities \(x^2+y^2+(z-1)^2\le 2\) and \(x^2+y^2+(z+1)^2\le 2\).
  • Exercises: 3.6.8, 4.1.3, 4.1.7
• HWA-12, due Mon, Nov 14.
  • Find the area bounded by the loop \((\sin t,\sin 2t)\) for \(0\le t\le \pi\).
  • Exercises: 4.1.13, 4.2.4, 4.2.8, 4.2.9
• HWA-13, due Mon, Nov 28.
  • Is there a potential for the vector field \(\mathbf{f}(x,y)=\tfrac{x}{(x^2+y^2)^2}\mathbf{i}+\tfrac{y}{(x^2+y^2)^2}\mathbf{j}\)?
  • Exercises: 4.2.5, 4.2.10, 4.3.3, 4.3.11
• HWA-14, due Mon, Dec 5.
  • Exercises: 4.4.1, 4.4.5, 4.5.5, 4.5.12, 4.6.20
• Practice exam
  • Exercises: 1.8.10, 2.3.7, 2.5.2, 2.7.1, 3.5.10, 4.2.10, 4.6.19
  • Show that
    \(~\oint\limits_C (f\mathbf{i}-y\nabla f)\cdot d\mathbf{r}=\oint\limits_C (f\mathbf{j}-x\nabla f)\cdot d\mathbf{r} \)
    for any closed curve \(C\) and any smooth function \(f\) defined on \(\mathbb{R}^3\)
• Final Exam, Dec. 12, 4:40--6:30pm, 165 Willard
  • 8 problems
  • Solution of problems from the quizzes ,
  • Few problems about curves.