Problem books of applications of calculus 1

[Akitirija]

Hi there, everyone!

I'm sure this question has been asked many times before, but I did not really find any similar posts, so I hope you guys will bear with me!

I am teaching myself what could be categorized as Calculus 1, using Adams' "Calculus: A Complete Course" along with "Schaum's 3000 Solved Problems in Calculus" and The Great Courses' "Understanding Calculus - Problems, Solutions, And Tips".

I am beginning to become very passionate about mathematics, although I want to study engineering. I am really, really missing a "book of problems" of calculus 1 with applications for engineers, and I wondered if you had any suggestions? They should include answers (and preferably solutions).

For me, the greatest motivation in mathematics are challenging, but still-possible-to-solve, problems, and I find mathematics to be highly interesting when I can apply what I learn.

I would really, really appreciate your input here!

 

[Quantum Braket]

Look for an elementary text on statics (calculus based) and work through the problems. Schaums has many such books with worked problems.
Any calc based physics text would be fount of problems.

 

[Akitirija]

Thank your for the answer, Quantum Braket. I was not being very clear in my question. I was thinking more about a book that follows to some extent the curriculum of Calculus 1. For example, first chapter consisting of limit problems that can be applied in "real life".

A physics text would also be very interesting, do you have any suggestions for a "novice"?

 

[Quantum Braket]

If you want calculus based books, Gasiorowicz or Serway are the usual freshman texts. Look for any book that has in its title "Physics for scientists and engineers" and you will get that. Also, get 3000 solved problems in Physics from Schaums.
The Schaums breaks things down into Algebra based and Calculus based problems.

Note that calculus is the language of physics, invented for physics by a physicist. =)
It is the most natural expression of physics. If you can do derivatives and simple integrals you can do most of a freshman physics text.

Online resources are at Khan Academy, which is very nice for the basics of calculus and physics.

Good luck!

 

[Akitirija]

Thank you very much, Quantum Braket! I will check out 3000 solved problems in Physics, it sounds like just the book I am looking for.

 

[Will Flannery]

I'll recommend my book, Mathematical Modeling and Computational Calculus, you can check out a synopsis at

www.berkeleyscience.com/mmcc.htm

There are 3 problems with every other calculus book :), ..
1. too difficult
2. too abstract
3. you can't solve any problems with what you learn

All these problems are because analytic calculus is difficult, abstract, and you can do very little with it until very late in the game ... using the Laplace transform, etc. Even then its usually impossible to solve a problem analytically. Example - Newton developed calculus to solve the differential equation r'' = C/(r*r), which characterizes the trajectory of a falling object. You won't be able to solve it analytically no matter how many courses you take as no analytic solution exists.

Now problems are solved using what I call computational calculus and what your textbook calls numeric methods for solving differential equations. The mathematicians can make it difficult, but in its simplest form it amounts to repeated application of the formula distance = velocity times time, i.e. it is trivially easy, and you can do all sorts of interesting projects, as described in MMCC I. For example you can compute solutions to r'' = C/(r*r) no problem to calculate satellite orbits, rocket trajectories, etc. From my experience (engineer for 20 years) this is the way it's done in the real world.

 

[Akitirija]

Thank you for your suggestion, Flannery! I especially like the CWT Crying Towel :)

Unfortunately, after having leafed through some analytical calculus books, I have to agree with you about their problems being "unsolvable", at least for me.

 

[smodak]

Thank your for the answer, Quantum Braket. I was not being very clear in my question. I was thinking more about a book that follows to some extent the curriculum of Calculus 1. For example, first chapter consisting of limit problems that can be applied in "real life".

A physics text would also be very interesting, do you have any suggestions for a "novice"?

This book has a lot of nice problems but not sure if they are the kind you are looking for...

The Humongous Book of Calculus Problems - Kelley
https://www.amazon.com/dp/1592575129/?tag=pfamazon01-20